atlas> atlas> atlas> {an excellent question from Emile! The Big Green Book is in fact { > Representations of Real Reductive Groups, in the green Birkhauser series, 1981 { > I think there is supposed to be a new edition coming out...? { > } atlas> atlas> atlas> {welcome back...} atlas> atlas> atlas> G:=SO(4,2) Value: disconnected quasisplit real group with Lie algebra 'su(2,2)' atlas> B:=block_of (trivial(G)) Value: [final parameter (x=0,lambda=[2,1,0]/1,nu=[0,0,0]/1),final parameter (x=1,lambda=[2,1,0]/1,nu=[0,0,0]/1),final parameter (x=2,lambda=[2,1,0]/1,nu=[0,0,0]/1),final parameter (x=5,lambda=[2,1,0]/1,nu=[0,1,-1]/2),final parameter (x=4,lambda=[2,1,0]/1,nu=[1,-1,0]/2),final parameter (x=3,lambda=[2,1,0]/1,nu=[0,1,1]/2),final parameter (x=6,lambda=[2,1,0]/1,nu=[0,1,0]/1),final parameter (x=6,lambda=[2,2,1]/1,nu=[0,1,0]/1),final parameter (x=8,lambda=[2,1,0]/1,nu=[1,0,-1]/1),final parameter (x=7,lambda=[2,1,0]/1,nu=[1,0,1]/1),final parameter (x=9,lambda=[2,1,0]/1,nu=[2,0,0]/1),final parameter (x=9,lambda=[3,1,1]/1,nu=[2,0,0]/1),final parameter (x=10,lambda=[2,1,0]/1,nu=[3,3,0]/2),final parameter (x=11,lambda=[2,1,0]/1,nu=[2,1,0]/1),final parameter (x=11,lambda=[3,2,0]/1,nu=[2,1,0]/1)] atlas> #B Value: 15 atlas> for p in B do let (P,)=cuspidal_data (p) in let M=Levi(P) in prints(M) od disconnected quasisplit real group with Lie algebra 'su(2,2)' disconnected quasisplit real group with Lie algebra 'su(2,2)' disconnected quasisplit real group with Lie algebra 'su(2,2)' disconnected quasisplit real group with Lie algebra 'sl(2,R).u(1).gl(1,R)' disconnected quasisplit real group with Lie algebra 'sl(2,R).u(1).gl(1,R)' disconnected quasisplit real group with Lie algebra 'sl(2,R).u(1).gl(1,R)' disconnected quasisplit real group with Lie algebra 'u(1).gl(1,R).gl(1,R)' disconnected quasisplit real group with Lie algebra 'u(1).gl(1,R).gl(1,R)' disconnected quasisplit real group with Lie algebra 'sl(2,R).u(1).gl(1,R)' disconnected quasisplit real group with Lie algebra 'sl(2,R).u(1).gl(1,R)' disconnected quasisplit real group with Lie algebra 'u(1).gl(1,R).gl(1,R)' disconnected quasisplit real group with Lie algebra 'u(1).gl(1,R).gl(1,R)' disconnected quasisplit real group with Lie algebra 'sl(2,R).u(1).gl(1,R)' disconnected quasisplit real group with Lie algebra 'u(1).gl(1,R).gl(1,R)' disconnected quasisplit real group with Lie algebra 'u(1).gl(1,R).gl(1,R)' Value: [(),(),(),(),(),(),(),(),(),(),(),(),(),(),()] atlas> {G=SO(4,2)} atlas> atlas> {M=SO(3,1)xGL(1,R)} atlas> {M=SO(2,0)xGL(1,R)^2} atlas> atlas> atlas> G:=SO(5,1) Value: disconnected real group with Lie algebra 'sl(2,H)' atlas> set B=block_of (trivial(G)) Identifier B: [Param] (hiding previous one of type [Param]) atlas> for p in B do let (P,)=cuspidal_data (p) in let M=Levi(P) in prints(M) od disconnected real group with Lie algebra 'su(2).su(2).gl(1,R)' disconnected real group with Lie algebra 'su(2).su(2).gl(1,R)' disconnected real group with Lie algebra 'su(2).su(2).gl(1,R)' Value: [(),(),()] atlas> {M=SO(4)xGL(1,R)} atlas> atlas> atlas> atlas> atlas> set G=Sp(4,R) Identifier G: RealForm (hiding previous one of type RealForm) atlas> set B=block_of (trivial(G)) Identifier B: [Param] (hiding previous one of type [Param]) atlas> set p=B[4] Identifier p: Param (hiding previous one of type Param) atlas> set (P,sigma)=cuspidal_data (p) Identifiers P: ([int],KGBElt) (hiding previous one of type ([int],KGBElt)), sigma: Param (hiding previous one of type Param) atlas> Levi(P) Value: disconnected split real group with Lie algebra 'sl(2,R).gl(1,R)' atlas> sigma Value: final parameter (x=0,lambda=[1,2]/1,nu=[1,0]/1) atlas> atlas> atlas> induce_standard (sigma,P,G) Value: 1*final parameter (x=5,lambda=[2,1]/1,nu=[0,1]/1) atlas> p Value: final parameter (x=5,lambda=[2,1]/1,nu=[0,1]/1) atlas> {inducing discrete series from P to G} atlas> atlas> {induce any irreducible} atlas> atlas> set M=Levi(P) Identifier M: RealForm (hiding previous one of type RealForm) atlas> set pM=trivial(M) Identifier pM: Param atlas> pM Value: final parameter (x=2,lambda=[0,1]/1,nu=[0,1]/1) atlas> infinitesimal_character (pM) Value: [ 0, 1 ]/1 atlas> induce_irreducible (pM,P,G) {induce irreducible from SL(2,R)xGL(1,R) to Sp(4,R)} Value: 1*final parameter (x=4,lambda=[1,0]/1,nu=[1,-1]/2) 1*final parameter (x=10,lambda=[2,1]/1,nu=[1,0]/1) atlas> {example: spherical unitary dual of Sp(4,R): corner nu=[1,0]} atlas> atlas> atlas> atlas> G:=SL(2,R) Value: connected split real group with Lie algebra 'sl(2,R)' atlas> print_block(trivial(G)) Parameter defines element 2 of the following block: 0: 0 [i1] 1 (2,*) *(x=0,lam=rho+ [0], nu= [0]/1) e 1: 0 [i1] 0 (2,*) *(x=1,lam=rho+ [0], nu= [0]/1) e 2: 1 [r1] 2 (0,1) *(x=2,lam=rho+ [0], nu= [1]/1) 1^e atlas> atlas> atlas> set p=trivial(G) Identifier p: Param (hiding previous one of type Param) atlas> atlas> atlas> set irr=J(p) Identifier irr: (Param,string) (hiding previous one of type (Param,string)) atlas> set std=I(p) Identifier std: (Param,string) (hiding previous one of type string (constant)) atlas> show(irr) J(x=2,lambda=[1/1],nu=[1/1]) atlas> show(std) I(x=2,lambda=[1/1],nu=[1/1]) atlas> {induced from GL(1) to SL(2,R) = sum of 2 DS plus trivial} atlas> atlas> show(composition(std)) Error during analysis of expression at :252:0-22 Undefined identifier 'composition' Type check failed atlas> show(composition_series(std)) 1*J(x=0,lambda=[1/1],nu=[0/1]) 1*J(x=1,lambda=[1/1],nu=[0/1]) 1*J(x=2,lambda=[1/1],nu=[1/1]) atlas> set B=block_of (trivial(G)) Identifier B: [Param] (hiding previous one of type [Param]) atlas> show(composition_series (I(B[0]))) 1*J(x=0,lambda=[1/1],nu=[0/1]) atlas> show(composition_series (I(B[1]))) 1*J(x=1,lambda=[1/1],nu=[0/1]) atlas> show(composition_series (I(B[2]))) 1*J(x=0,lambda=[1/1],nu=[0/1]) 1*J(x=1,lambda=[1/1],nu=[0/1]) 1*J(x=2,lambda=[1/1],nu=[1/1]) atlas> atlas> atlas> atlas> show(character_formula (J(B[0]))) 1*I(x=0,lambda=[1/1],nu=[0/1]) atlas> show(J(B[0])) J(x=0,lambda=[1/1],nu=[0/1]) atlas> show(J(B[1])) J(x=1,lambda=[1/1],nu=[0/1]) atlas> show(J(B[2])) J(x=2,lambda=[1/1],nu=[1/1]) atlas> show(character_formula(J(B[2]))) -1*I(x=0,lambda=[1/1],nu=[0/1]) -1*I(x=1,lambda=[1/1],nu=[0/1]) 1*I(x=2,lambda=[1/1],nu=[1/1]) atlas> set M=KL_P_polynomials (B) Identifier M: [[vec]] (hiding previous one of type RealForm) atlas> M Value: [[[ 1 ],[ ],[ -1 ]],[[ ],[ 1 ],[ -1 ]],[[ ],[ ],[ 1 ]]] atlas> printPolyMatrix (M) +1 0 -1 0 +1 -1 0 0 +1 atlas> set m=KL_Q_polynomials (B) Identifier m: [[vec]] atlas> printPolyMatrix (m) +1 0 +1 0 +1 +1 0 0 +1 atlas> printPolyMatrix (m*M) +1 0 0 0 +1 0 0 0 +1 atlas> printPolyMatrix (M*m) +1 0 0 0 +1 0 0 0 +1 atlas> atlas> atlas> atlas> G:=Sp(4,R) Value: connected split real group with Lie algebra 'sp(4,R)' atlas> B:=block_of (trivial(G)) Value: [final parameter (x=0,lambda=[2,1]/1,nu=[0,0]/1),final parameter (x=1,lambda=[2,1]/1,nu=[0,0]/1),final parameter (x=2,lambda=[2,1]/1,nu=[0,0]/1),final parameter (x=3,lambda=[2,1]/1,nu=[0,0]/1),final parameter (x=5,lambda=[2,1]/1,nu=[0,1]/1),final parameter (x=6,lambda=[2,1]/1,nu=[0,1]/1),final parameter (x=4,lambda=[2,1]/1,nu=[1,-1]/2),final parameter (x=7,lambda=[2,1]/1,nu=[2,0]/1),final parameter (x=8,lambda=[2,1]/1,nu=[2,0]/1),final parameter (x=9,lambda=[2,1]/1,nu=[3,3]/2),final parameter (x=10,lambda=[2,1]/1,nu=[2,1]/1),final parameter (x=10,lambda=[3,2]/1,nu=[2,1]/1)] atlas> set M=KL_P_polynomials (B) Identifier M: [[vec]] (hiding previous one of type [[vec]]) atlas> set m=KL_Q_polynomials (B) Identifier m: [[vec]] (hiding previous one of type [[vec]]) atlas> printPolyMatrix (M) +1 0 0 0 -1 0 -1 +1 +1 +1 -1 0 0 +1 0 0 0 -1 -1 +1 +1 +1 -1 0 0 0 +1 0 -1 0 0 +1 0 +1 -1 -q 0 0 0 +1 0 -1 0 0 +1 +1 -1 -q 0 0 0 0 +1 0 0 -1 0 -1 +1 0 0 0 0 0 0 +1 0 0 -1 -1 +1 0 0 0 0 0 0 0 +1 -1 -1 -1 +1 0 0 0 0 0 0 0 0 +1 0 0 -1 0 0 0 0 0 0 0 0 0 +1 0 -1 0 0 0 0 0 0 0 0 0 0 +1 -1 -1 0 0 0 0 0 0 0 0 0 0 +1 0 0 0 0 0 0 0 0 0 0 0 0 +1 atlas> show(character_formula (J(trivial(G))) ( > ) -1*I(x=0,lambda=[2/1,1/1],nu=[0/1,0/1]) -1*I(x=1,lambda=[2/1,1/1],nu=[0/1,0/1]) -1*I(x=2,lambda=[2/1,1/1],nu=[0/1,0/1]) -1*I(x=3,lambda=[2/1,1/1],nu=[0/1,0/1]) 1*I(x=4,lambda=[2/1,1/1],nu=[1/2,-1/2]) 1*I(x=5,lambda=[2/1,1/1],nu=[0/1,1/1]) 1*I(x=6,lambda=[2/1,1/1],nu=[0/1,1/1]) -1*I(x=7,lambda=[2/1,1/1],nu=[2/1,0/1]) -1*I(x=8,lambda=[2/1,1/1],nu=[2/1,0/1]) -1*I(x=9,lambda=[2/1,1/1],nu=[3/2,3/2]) 1*I(x=10,lambda=[2/1,1/1],nu=[2/1,1/1]) atlas> atlas> atlas> atlas> {KL_P_polynomials(B): column #j, evaluate at q=1, gives character formula for J(#j), { > as a sum of standard modules} atlas> atlas> {KL_Q_polynomials(B): column #j, evaluate at q=1, gives composition series for I(#j), { > as a sum of irreducibles} atlas> atlas> printPolyMatrix (M) +1 0 0 0 -1 0 -1 +1 +1 +1 -1 0 0 +1 0 0 0 -1 -1 +1 +1 +1 -1 0 0 0 +1 0 -1 0 0 +1 0 +1 -1 -q 0 0 0 +1 0 -1 0 0 +1 +1 -1 -q 0 0 0 0 +1 0 0 -1 0 -1 +1 0 0 0 0 0 0 +1 0 0 -1 -1 +1 0 0 0 0 0 0 0 +1 -1 -1 -1 +1 0 0 0 0 0 0 0 0 +1 0 0 -1 0 0 0 0 0 0 0 0 0 +1 0 -1 0 0 0 0 0 0 0 0 0 0 +1 -1 -1 0 0 0 0 0 0 0 0 0 0 +1 0 0 0 0 0 0 0 0 0 0 0 0 +1 atlas> atlas> atlas> printPolyMatrix (m) +1 0 0 0 +1 0 +1 +1 0 +1 +1 +1 0 +1 0 0 0 +1 +1 0 +1 +1 +1 +1 0 0 +1 0 +1 0 0 0 0 0 0 +q 0 0 0 +1 0 +1 0 0 0 0 0 +q 0 0 0 0 +1 0 0 +1 0 +1 +1 +1 0 0 0 0 0 +1 0 0 +1 +1 +1 +1 0 0 0 0 0 0 +1 +1 +1 +1 +2 +1 0 0 0 0 0 0 0 +1 0 0 +1 0 0 0 0 0 0 0 0 0 +1 0 +1 0 0 0 0 0 0 0 0 0 0 +1 +1 +1 0 0 0 0 0 0 0 0 0 0 +1 0 0 0 0 0 0 0 0 0 0 0 0 +1 atlas> show(composition_series (I(trivial(G)))) 1*J(x=0,lambda=[2/1,1/1],nu=[0/1,0/1]) 1*J(x=1,lambda=[2/1,1/1],nu=[0/1,0/1]) 2*J(x=4,lambda=[2/1,1/1],nu=[1/2,-1/2]) 1*J(x=5,lambda=[2/1,1/1],nu=[0/1,1/1]) 1*J(x=6,lambda=[2/1,1/1],nu=[0/1,1/1]) 1*J(x=7,lambda=[2/1,1/1],nu=[2/1,0/1]) 1*J(x=8,lambda=[2/1,1/1],nu=[2/1,0/1]) 1*J(x=9,lambda=[2/1,1/1],nu=[3/2,3/2]) 1*J(x=10,lambda=[2/1,1/1],nu=[2/1,1/1]) atlas> printPolyMatrix (M*m) +1 0 0 0 0 0 0 0 0 0 0 0 0 +1 0 0 0 0 0 0 0 0 0 0 0 0 +1 0 0 0 0 0 0 0 0 0 0 0 0 +1 0 0 0 0 0 0 0 0 0 0 0 0 +1 0 0 0 0 0 0 0 0 0 0 0 0 +1 0 0 0 0 0 0 0 0 0 0 0 0 +1 0 0 0 0 0 0 0 0 0 0 0 0 +1 0 0 0 0 0 0 0 0 0 0 0 0 +1 0 0 0 0 0 0 0 0 0 0 0 0 +1 0 0 0 0 0 0 0 0 0 0 0 0 +1 0 0 0 0 0 0 0 0 0 0 0 0 +1 atlas> printPolyMatrix (M) +1 0 0 0 -1 0 -1 +1 +1 +1 -1 0 0 +1 0 0 0 -1 -1 +1 +1 +1 -1 0 0 0 +1 0 -1 0 0 +1 0 +1 -1 -q 0 0 0 +1 0 -1 0 0 +1 +1 -1 -q 0 0 0 0 +1 0 0 -1 0 -1 +1 0 0 0 0 0 0 +1 0 0 -1 -1 +1 0 0 0 0 0 0 0 +1 -1 -1 -1 +1 0 0 0 0 0 0 0 0 +1 0 0 -1 0 0 0 0 0 0 0 0 0 +1 0 -1 0 0 0 0 0 0 0 0 0 0 +1 -1 -1 0 0 0 0 0 0 0 0 0 0 +1 0 0 0 0 0 0 0 0 0 0 0 0 +1 atlas> set p=B[11] Identifier p: Param (hiding previous one of type Param) atlas> show(character_formula (J(p))) -1*I(x=2,lambda=[2/1,1/1],nu=[0/1,0/1]) -1*I(x=3,lambda=[2/1,1/1],nu=[0/1,0/1]) -1*I(x=9,lambda=[2/1,1/1],nu=[3/2,3/2]) 1*I(x=10,lambda=[3/1,2/1],nu=[2/1,1/1]) atlas> atlas> atlas> atlas> {fact: polynomial in q: tells you about levels where things occur in the Jantzen filtration} atlas> atlas> atlas> G:=SO(4,4) Value: disconnected split real group with Lie algebra 'so(4,4)' atlas> B:=block_of (trivial(G))) ^ syntax error, unexpected ')', expecting '\n' atlas> B:=block_of (trivial(G)) atlas> #B Value: 96 atlas> set M=KL_P_polynomials (B) Identifier M: [[vec]] (hiding previous one of type [[vec]]) atlas> set m=KL_Q_polynomials (B) print_P Identifier m: [[vec]] (hiding previous one of type [[vec]]) atlas> printPolyMatrix (M) +1 0 0 0 0 0 -1 0 -1 0 -1 0 -1 0 +1 0 +1 0 +1 0 +1 +1 +1 0 0 +1 -1 -1 0 0 -1 -1 -2 0 -1 -1 -1 -1 -1 -1 +1 +1 0 0 +1 +1 +1+q +1+q +1 +2 +2 +1 +2+q +1 +1 +2+q -1 -1 -1 -1 -1-q -1-q -2 -2-3q -2 -2 -1-q -1-q -1-q -1-q +1+q +1+q +1 +1 +1+2q +1+2q +1+2q +1+2q +2+q +2+q +1+2q +1+2q -1-q -1-q -1-q -1-q -1 -1 -1-q -1-q +1 +3q +q+q^3 +3q +1 +q+q^3 0 +1 0 0 0 0 0 0 0 -1 -1 0 0 -1 0 +1 +1 0 0 +1 +1 0 0 +1 +1 +1 0 0 -1-q -1-q -1 -1 0 -2 -1 -1 -1-q -1 -1 -1-q 0 0 +1 +1 +1 +1 +1+q +1+q +1 +2 +2 +1 +2+q +1+q +1+q +2+q -1 -1 -1 -1 -1-q -1-q -2 -2-2q -2-2q -2 -1-q -1-q -1-q -1-q +1+q +1+q +1 +1 +1+2q +1+2q +1+2q +1+2q +2+q +2+q +1+2q +1+2q -1-q -1-q -1-q -1-q -1 -1 -1-q -1-q +1 +3q +q +3q +1 +q 0 0 +1 0 0 0 -1 0 0 0 0 0 0 0 +1 0 +1 0 +1 0 0 0 0 0 0 0 -1 -1 0 0 -1-q 0 -1-q 0 -1-q 0 -1 0 0 -1 +1 +1 0 0 +1+q +1+q 0 0 +1 +1+2q 0 +1 +1+q +1 +1 +1+q -1-q -1-q 0 0 -1-q -1-q -1-q -2-3q -2 -1-q -1-q -1-q -1-q -1-q +1+q +1+q +1 +1 +1+q+q^2 +1+q+q^2 +1+q+q^2 +1+q+q^2 +2+q +2+q +1+q+q^2 +1+q+q^2 -1-q -1-q -1-q -1-q -1-q^3 -1-q^3 -1-q -1-q +1 +2q+q^2 +q+q^3 +2q+q^2 +1 +q+q^3 0 0 0 +1 0 0 0 0 -1 0 0 -1 -1 0 +1 0 0 +1 +1 0 +1 +1 +1 0 0 +1 -1-q -1-q 0 0 -1 -1 -2 0 -1 -1 -1-q -1 -1 -1-q +1 +1 0 0 +1+q +1+q +1 +1 +1 +2 +2 +1 +2+q +1+q +1+q +2+q -1 -1 -1 -1 -1-q -1-q -2 -2-2q -2-2q -2 -1-q -1-q -1-q -1-q +1 +1 +1+q +1+q +1+2q +1+2q +1+2q +1+2q +2+q +2+q +1+2q +1+2q -1-q -1-q -1-q -1-q -1 -1 -1-q -1-q +1 +3q +q +3q +1 +q 0 0 0 0 +1 0 0 -1 0 -1 0 -1 0 -1 0 +1 0 +1 0 +1 +1 0 0 +1 +1 +1 0 0 -1 -1 -1 -1 0 -2 -1 -1 -1 -1 -1 -1 0 0 +1 +1 +1+q +1+q +1 +1 +1 +2 +2 +1 +2+q +1 +1 +2+q -1 -1 -1 -1 -1-q -1-q -2 -2 -2-3q -2 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0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +1 0 0 0 0 0 +1 0 0 +1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +1 0 0 0 +1 0 +1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +1 0 0 0 0 0 0 +1 +1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +1 0 +1 +1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +1 0 0 0 +1 +1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +1 atlas> set p=trivial(G) Identifier p: Param (hiding previous one of type Param) atlas> show(composition_series (I(p))) 1*J(x=0,lambda=[3/1,2/1,1/1,0/1],nu=[0/1,0/1,0/1,0/1]) 3*J(x=1,lambda=[3/1,2/1,1/1,0/1],nu=[0/1,0/1,0/1,0/1]) 2*J(x=2,lambda=[3/1,2/1,1/1,0/1],nu=[0/1,0/1,0/1,0/1]) 3*J(x=3,lambda=[3/1,2/1,1/1,0/1],nu=[0/1,0/1,0/1,0/1]) 1*J(x=4,lambda=[3/1,2/1,1/1,0/1],nu=[0/1,0/1,0/1,0/1]) 2*J(x=5,lambda=[3/1,2/1,1/1,0/1],nu=[0/1,0/1,0/1,0/1]) 2*J(x=6,lambda=[3/1,2/1,1/1,0/1],nu=[0/1,0/1,1/2,1/2]) 2*J(x=7,lambda=[3/1,2/1,1/1,0/1],nu=[0/1,0/1,1/2,1/2]) 1*J(x=8,lambda=[3/1,2/1,1/1,0/1],nu=[0/1,1/2,-1/2,0/1]) 1*J(x=9,lambda=[3/1,2/1,1/1,0/1],nu=[0/1,1/2,-1/2,0/1]) 2*J(x=10,lambda=[3/1,2/1,1/1,0/1],nu=[0/1,0/1,1/2,-1/2]) 2*J(x=11,lambda=[3/1,2/1,1/1,0/1],nu=[0/1,0/1,1/2,-1/2]) 2*J(x=12,lambda=[3/1,2/1,1/1,0/1],nu=[1/2,-1/2,0/1,0/1]) 2*J(x=13,lambda=[3/1,2/1,1/1,0/1],nu=[1/2,-1/2,0/1,0/1]) 2*J(x=14,lambda=[3/1,2/1,1/1,0/1],nu=[0/1,0/1,1/1,0/1]) 1*J(x=14,lambda=[3/1,2/1,2/1,1/1],nu=[0/1,0/1,1/1,0/1]) 2*J(x=15,lambda=[3/1,2/1,1/1,0/1],nu=[0/1,0/1,1/1,0/1]) 1*J(x=15,lambda=[3/1,2/1,2/1,1/1],nu=[0/1,0/1,1/1,0/1]) 3*J(x=16,lambda=[3/1,2/1,1/1,0/1],nu=[1/2,-1/2,1/2,1/2]) 3*J(x=17,lambda=[3/1,2/1,1/1,0/1],nu=[1/2,-1/2,1/2,-1/2]) 3*J(x=18,lambda=[3/1,2/1,1/1,0/1],nu=[0/1,1/1,0/1,1/1]) 3*J(x=19,lambda=[3/1,2/1,1/1,0/1],nu=[0/1,1/1,0/1,1/1]) 3*J(x=20,lambda=[3/1,2/1,1/1,0/1],nu=[0/1,1/1,0/1,-1/1]) 3*J(x=21,lambda=[3/1,2/1,1/1,0/1],nu=[0/1,1/1,0/1,-1/1]) 3*J(x=22,lambda=[3/1,2/1,1/1,0/1],nu=[1/1,0/1,-1/1,0/1]) 3*J(x=23,lambda=[3/1,2/1,1/1,0/1],nu=[1/1,0/1,-1/1,0/1]) 5*J(x=24,lambda=[3/1,2/1,1/1,0/1],nu=[1/2,-1/2,1/1,0/1]) 2*J(x=24,lambda=[3/1,2/1,2/1,-1/1],nu=[1/2,-1/2,1/1,0/1]) 2*J(x=25,lambda=[3/1,2/1,1/1,0/1],nu=[1/1,1/1,-1/1,1/1]) 1*J(x=26,lambda=[3/1,2/1,1/1,0/1],nu=[0/1,2/1,0/1,0/1]) 1*J(x=26,lambda=[3/1,3/1,1/1,1/1],nu=[0/1,2/1,0/1,0/1]) 1*J(x=27,lambda=[3/1,2/1,1/1,0/1],nu=[0/1,2/1,0/1,0/1]) 1*J(x=27,lambda=[3/1,3/1,1/1,1/1],nu=[0/1,2/1,0/1,0/1]) 2*J(x=28,lambda=[3/1,2/1,1/1,0/1],nu=[1/1,1/1,-1/1,-1/1]) 2*J(x=29,lambda=[3/1,2/1,1/1,0/1],nu=[0/1,3/2,3/2,0/1]) 2*J(x=30,lambda=[3/1,2/1,1/1,0/1],nu=[0/1,3/2,3/2,0/1]) 2*J(x=31,lambda=[3/1,2/1,1/1,0/1],nu=[3/2,0/1,0/1,3/2]) 2*J(x=32,lambda=[3/1,2/1,1/1,0/1],nu=[3/2,0/1,0/1,3/2]) 2*J(x=33,lambda=[3/1,2/1,1/1,0/1],nu=[3/2,0/1,0/1,-3/2]) 2*J(x=34,lambda=[3/1,2/1,1/1,0/1],nu=[3/2,0/1,0/1,-3/2]) 2*J(x=35,lambda=[3/1,2/1,1/1,0/1],nu=[1/1,2/1,-1/1,0/1]) 2*J(x=35,lambda=[3/1,3/1,1/1,-1/1],nu=[1/1,2/1,-1/1,0/1]) 1*J(x=36,lambda=[3/1,2/1,1/1,0/1],nu=[3/2,3/2,3/2,3/2]) 1*J(x=37,lambda=[3/1,2/1,1/1,0/1],nu=[3/2,3/2,3/2,-3/2]) 1*J(x=38,lambda=[3/1,2/1,1/1,0/1],nu=[0/1,2/1,1/1,0/1]) 2*J(x=38,lambda=[3/1,3/1,2/1,0/1],nu=[0/1,2/1,1/1,0/1]) 1*J(x=39,lambda=[3/1,2/1,1/1,0/1],nu=[0/1,2/1,1/1,0/1]) 2*J(x=39,lambda=[3/1,3/1,2/1,0/1],nu=[0/1,2/1,1/1,0/1]) 3*J(x=40,lambda=[3/1,2/1,1/1,0/1],nu=[3/2,1/2,-1/2,3/2]) 1*J(x=41,lambda=[3/1,2/1,1/1,0/1],nu=[3/1,0/1,0/1,0/1]) 1*J(x=42,lambda=[3/1,2/1,1/1,0/1],nu=[3/1,0/1,0/1,0/1]) 3*J(x=43,lambda=[3/1,2/1,1/1,0/1],nu=[3/2,1/2,-1/2,-3/2]) 1*J(x=44,lambda=[3/1,2/1,1/1,0/1],nu=[2/1,0/1,2/1,0/1]) 1*J(x=45,lambda=[3/1,2/1,1/1,0/1],nu=[2/1,0/1,2/1,0/1]) 1*J(x=46,lambda=[3/1,2/1,1/1,0/1],nu=[3/2,2/1,1/1,3/2]) 1*J(x=46,lambda=[3/1,3/1,2/1,0/1],nu=[3/2,2/1,1/1,3/2]) 1*J(x=47,lambda=[3/1,2/1,1/1,0/1],nu=[3/2,2/1,1/1,-3/2]) 1*J(x=47,lambda=[3/1,3/1,0/1,0/1],nu=[3/2,2/1,1/1,-3/2]) 2*J(x=48,lambda=[3/1,2/1,1/1,0/1],nu=[3/1,1/2,-1/2,0/1]) 1*J(x=49,lambda=[3/1,2/1,1/1,0/1],nu=[2/1,1/1,2/1,1/1]) 1*J(x=50,lambda=[3/1,2/1,1/1,0/1],nu=[2/1,1/1,2/1,-1/1]) 1*J(x=51,lambda=[3/1,2/1,1/1,0/1],nu=[3/1,0/1,1/1,0/1]) 1*J(x=52,lambda=[3/1,2/1,1/1,0/1],nu=[3/1,0/1,1/1,0/1]) 1*J(x=53,lambda=[3/1,2/1,1/1,0/1],nu=[5/2,5/2,0/1,0/1]) 1*J(x=54,lambda=[3/1,2/1,1/1,0/1],nu=[5/2,5/2,0/1,0/1]) 1*J(x=55,lambda=[3/1,2/1,1/1,0/1],nu=[2/1,2/1,2/1,0/1]) 1*J(x=56,lambda=[3/1,2/1,1/1,0/1],nu=[3/1,1/1,1/1,1/1]) 1*J(x=57,lambda=[3/1,2/1,1/1,0/1],nu=[3/1,1/1,1/1,-1/1]) 1*J(x=58,lambda=[3/1,2/1,1/1,0/1],nu=[5/2,5/2,1/2,1/2]) 1*J(x=59,lambda=[3/1,2/1,1/1,0/1],nu=[5/2,5/2,1/2,-1/2]) 1*J(x=60,lambda=[3/1,2/1,1/1,0/1],nu=[3/1,2/1,0/1,0/1]) 1*J(x=61,lambda=[3/1,2/1,1/1,0/1],nu=[3/1,2/1,0/1,0/1]) 1*J(x=62,lambda=[3/1,2/1,1/1,0/1],nu=[5/2,5/2,1/1,0/1]) 1*J(x=63,lambda=[3/1,2/1,1/1,0/1],nu=[3/1,2/1,1/2,1/2]) 1*J(x=64,lambda=[3/1,2/1,1/1,0/1],nu=[3/1,3/2,3/2,0/1]) 1*J(x=65,lambda=[3/1,2/1,1/1,0/1],nu=[3/1,2/1,1/2,-1/2]) 1*J(x=66,lambda=[3/1,2/1,1/1,0/1],nu=[3/1,2/1,1/1,0/1]) atlas> p Value: final parameter (x=66,lambda=[3,2,1,0]/1,nu=[3,2,1,0]/1) atlas> show(I(p)) I(x=66,lambda=[3/1,2/1,1/1,0/1],nu=[3/1,2/1,1/1,0/1]) atlas> set cs=composition_series (p) Identifier cs: ParamPol atlas> #cs Value: 77 atlas> #B Value: 96 atlas> print_block(trivial(G)) Parameter defines element 90 of the following block: 0: 0 [i1,i1,i1,i1] 1 2 3 3 (10, *) ( 6, *) (12, *) ( 8, *) *(x= 0,lam=rho+ [0,0,0,0], nu= [0,0,0,0]/1) e 1: 0 [i1,ic,i1,i1] 0 1 4 4 (10, *) ( *, *) (13, *) ( 9, *) *(x= 1,lam=rho+ [0,0,0,0], nu= [0,0,0,0]/1) e 2: 0 [ic,i1,ic,ic] 2 0 2 2 ( *, *) ( 6, *) ( *, *) ( *, *) *(x= 2,lam=rho+ [0,0,0,0], nu= [0,0,0,0]/1) e 3: 0 [i1,ic,i1,i1] 4 3 0 0 (11, *) ( *, *) (12, *) ( 8, *) *(x= 3,lam=rho+ [0,0,0,0], nu= [0,0,0,0]/1) e 4: 0 [i1,i1,i1,i1] 3 5 1 1 (11, *) ( 7, *) (13, *) ( 9, *) *(x= 4,lam=rho+ [0,0,0,0], nu= [0,0,0,0]/1) e 5: 0 [ic,i1,ic,ic] 5 4 5 5 ( *, *) ( 7, *) ( *, *) ( *, *) *(x= 5,lam=rho+ [0,0,0,0], nu= [0,0,0,0]/1) e 6: 1 [C+,r1,C+,C+] 16 6 18 14 ( *, *) ( 0, 2) ( *, *) ( *, *) *(x= 8,lam=rho+ [0,0,0,0], nu= [0,1,-1,0]/2) 2^e 7: 1 [C+,r1,C+,C+] 17 7 19 15 ( *, *) ( 4, 5) ( *, *) ( *, *) *(x= 9,lam=rho+ [0,0,0,0], nu= [0,1,-1,0]/2) 2^e 8: 1 [i1,C+,i2,r1] 9 14 8 8 (20, *) ( *, *) (21,22) ( 0, 3) *(x= 6,lam=rho+ [0,0,0,0], nu= [0,0,1,1]/2) 4^e 9: 1 [i1,C+,i2,r1] 8 15 9 9 (20, *) ( *, *) (23,24) ( 1, 4) *(x= 7,lam=rho+ [0,0,0,0], nu= [0,0,1,1]/2) 4^e 10: 1 [r1,C+,i1,i1] 10 16 11 11 ( 0, 1) ( *, *) (25, *) (20, *) *(x=12,lam=rho+ [0,0,0,0], nu= [1,-1,0,0]/2) 1^e 11: 1 [r1,C+,i1,i1] 11 17 10 10 ( 3, 4) ( *, *) (25, *) (20, *) *(x=13,lam=rho+ [0,0,0,0], nu= [1,-1,0,0]/2) 1^e 12: 1 [i1,C+,r1,i2] 13 18 12 12 (25, *) ( *, *) ( 0, 3) (21,22) *(x=10,lam=rho+ [0,0,0,0], nu= [0,0,1,-1]/2) 3^e 13: 1 [i1,C+,r1,i2] 12 19 13 13 (25, *) ( *, *) ( 1, 4) (23,24) *(x=11,lam=rho+ [0,0,0,0], nu= [0,0,1,-1]/2) 3^e 14: 2 [C+,C-,C+,C-] 30 8 32 6 ( *, *) ( *, *) ( *, *) ( *, *) *(x=18,lam=rho+ [0,0,0,0], nu= [0,1,0,1]/1) 2x4^e 15: 2 [C+,C-,C+,C-] 31 9 33 7 ( *, *) ( *, *) ( *, *) ( *, *) *(x=19,lam=rho+ [0,0,0,0], nu= [0,1,0,1]/1) 2x4^e 16: 2 [C-,C-,C+,C+] 6 10 34 30 ( *, *) ( *, *) ( *, *) ( *, *) *(x=22,lam=rho+ [0,0,0,0], nu= [1,0,-1,0]/1) 1x2^e 17: 2 [C-,C-,C+,C+] 7 11 35 31 ( *, *) ( *, *) ( *, *) ( *, *) *(x=23,lam=rho+ [0,0,0,0], nu= [1,0,-1,0]/1) 1x2^e 18: 2 [C+,C-,C-,C+] 34 12 6 32 ( *, *) ( *, *) ( *, *) ( *, *) *(x=20,lam=rho+ [0,0,0,0], nu= [0,1,0,-1]/1) 2x3^e 19: 2 [C+,C-,C-,C+] 35 13 7 33 ( *, *) ( *, *) ( *, *) ( *, *) *(x=21,lam=rho+ [0,0,0,0], nu= [0,1,0,-1]/1) 2x3^e 20: 2 [r1,C+,i2,r1] 20 36 20 20 ( 8, 9) ( *, *) (37,38) (10,11) *(x=16,lam=rho+ [0,0,0,0], nu= [1,-1,1,1]/2) 1^4^e 21: 2 [i1,C+,r2,r2] 23 26 22 22 (37, *) ( *, *) ( 8, *) (12, *) *(x=14,lam=rho+ [0,0,0,0], nu= [0,0,1,0]/1) 3^4^e 22: 2 [i1,C+,r2,r2] 24 27 21 21 (38, *) ( *, *) ( 8, *) (12, *) *(x=14,lam=rho+[0,0,-1,-3], nu= [0,0,1,0]/1) 3^4^e 23: 2 [i1,C+,r2,r2] 21 28 24 24 (37, *) ( *, *) ( 9, *) (13, *) *(x=15,lam=rho+ [0,0,0,0], nu= [0,0,1,0]/1) 3^4^e 24: 2 [i1,C+,r2,r2] 22 29 23 23 (38, *) ( *, *) ( 9, *) (13, *) *(x=15,lam=rho+[0,0,-1,-3], nu= [0,0,1,0]/1) 3^4^e 25: 2 [r1,C+,r1,i2] 25 39 25 25 (12,13) ( *, *) (10,11) (37,38) *(x=17,lam=rho+ [0,0,0,0], nu=[1,-1,1,-1]/2) 1^3^e 26: 3 [C+,C-,C+,C+] 44 21 40 40 ( *, *) ( *, *) ( *, *) ( *, *) *(x=26,lam=rho+ [0,0,0,0], nu= [0,2,0,0]/1) 2x3^4^e 27: 3 [C+,C-,C+,C+] 45 22 41 41 ( *, *) ( *, *) ( *, *) ( *, *) *(x=26,lam=rho+[0,-1,0,-3], nu= [0,2,0,0]/1) 2x3^4^e 28: 3 [C+,C-,C+,C+] 46 23 42 42 ( *, *) ( *, *) ( *, *) ( *, *) *(x=27,lam=rho+ [0,0,0,0], nu= [0,2,0,0]/1) 2x3^4^e 29: 3 [C+,C-,C+,C+] 47 24 43 43 ( *, *) ( *, *) ( *, *) ( *, *) *(x=27,lam=rho+[0,-1,0,-3], nu= [0,2,0,0]/1) 2x3^4^e 30: 3 [C-,i1,C+,C-] 14 31 49 16 ( *, *) (48, *) ( *, *) ( *, *) *(x=31,lam=rho+ [0,0,0,0], nu= [3,0,0,3]/2) 1x2x4^e 31: 3 [C-,i1,C+,C-] 15 30 50 17 ( *, *) (48, *) ( *, *) ( *, *) *(x=32,lam=rho+ [0,0,0,0], nu= [3,0,0,3]/2) 1x2x4^e 32: 3 [C+,i2,C-,C-] 49 32 14 18 ( *, *) (40,41) ( *, *) ( *, *) *(x=29,lam=rho+ [0,0,0,0], nu= [0,3,3,0]/2) 3x2x4^e 33: 3 [C+,i2,C-,C-] 50 33 15 19 ( *, *) (42,43) ( *, *) ( *, *) *(x=30,lam=rho+ [0,0,0,0], nu= [0,3,3,0]/2) 3x2x4^e 34: 3 [C-,i1,C-,C+] 18 35 16 49 ( *, *) (51, *) ( *, *) ( *, *) *(x=33,lam=rho+ [0,0,0,0], nu= [3,0,0,-3]/2) 1x2x3^e 35: 3 [C-,i1,C-,C+] 19 34 17 50 ( *, *) (51, *) ( *, *) ( *, *) *(x=34,lam=rho+ [0,0,0,0], nu= [3,0,0,-3]/2) 1x2x3^e 36: 3 [C+,C-,C+,C+] 48 20 52 48 ( *, *) ( *, *) ( *, *) ( *, *) *(x=25,lam=rho+ [0,0,0,0], nu= [1,1,-1,1]/1) 2x1^4^e 37: 3 [r1,C+,r2,r2] 37 53 38 38 (21,23) ( *, *) (20, *) (25, *) *(x=24,lam=rho+ [0,0,0,0], nu= [1,-1,2,0]/2) 1^3^4^e 38: 3 [r1,C+,r2,r2] 38 54 37 37 (22,24) ( *, *) (20, *) (25, *) *(x=24,lam=rho+ [0,0,-1,1], nu= [1,-1,2,0]/2) 1^3^4^e 39: 3 [C+,C-,C+,C+] 51 25 51 55 ( *, *) ( *, *) ( *, *) ( *, *) *(x=28,lam=rho+ [0,0,0,0], nu=[1,1,-1,-1]/1) 2x1^3^e 40: 4 [C+,r2,C-,C-] 56 41 26 26 ( *, *) (32, *) ( *, *) ( *, *) *(x=38,lam=rho+ [0,0,0,0], nu= [0,2,1,0]/1) 2^3x2x4^e 41: 4 [C+,r2,C-,C-] 57 40 27 27 ( *, *) (32, *) ( *, *) ( *, *) *(x=38,lam=rho+[0,-1,-1,0], nu= [0,2,1,0]/1) 2^3x2x4^e 42: 4 [C+,r2,C-,C-] 58 43 28 28 ( *, *) (33, *) ( *, *) ( *, *) *(x=39,lam=rho+ [0,0,0,0], nu= [0,2,1,0]/1) 2^3x2x4^e 43: 4 [C+,r2,C-,C-] 59 42 29 29 ( *, *) (33, *) ( *, *) ( *, *) *(x=39,lam=rho+[0,-1,-1,0], nu= [0,2,1,0]/1) 2^3x2x4^e 44: 4 [C-,i1,C+,C+] 26 46 56 56 ( *, *) (60, *) ( *, *) ( *, *) *(x=41,lam=rho+ [0,0,0,0], nu= [3,0,0,0]/1) 1x2x3^4^e 45: 4 [C-,i1,C+,C+] 27 47 57 57 ( *, *) (61, *) ( *, *) ( *, *) *(x=41,lam=rho+[-1,0,0,-3], nu= [3,0,0,0]/1) 1x2x3^4^e 46: 4 [C-,i1,C+,C+] 28 44 58 58 ( *, *) (60, *) ( *, *) ( *, *) *(x=42,lam=rho+ [0,0,0,0], nu= [3,0,0,0]/1) 1x2x3^4^e 47: 4 [C-,i1,C+,C+] 29 45 59 59 ( *, *) (61, *) ( *, *) ( *, *) *(x=42,lam=rho+[-1,0,0,-3], nu= [3,0,0,0]/1) 1x2x3^4^e 48: 4 [C-,r1,C+,C-] 36 48 62 36 ( *, *) (30,31) ( *, *) ( *, *) *(x=40,lam=rho+ [0,0,0,0], nu= [3,1,-1,3]/2) 1x2x1^4^e 49: 4 [C-,C+,C-,C-] 32 63 30 34 ( *, *) ( *, *) ( *, *) ( *, *) *(x=44,lam=rho+ [0,0,0,0], nu= [2,0,2,0]/1) 1x3x2x4^e 50: 4 [C-,C+,C-,C-] 33 64 31 35 ( *, *) ( *, *) ( *, *) ( *, *) *(x=45,lam=rho+ [0,0,0,0], nu= [2,0,2,0]/1) 1x3x2x4^e 51: 4 [C-,r1,C-,C+] 39 51 39 65 ( *, *) (34,35) ( *, *) ( *, *) *(x=43,lam=rho+ [0,0,0,0], nu=[3,1,-1,-3]/2) 1x2x1^3^e 52: 4 [C+,i2,C-,C+] 62 52 36 62 ( *, *) (66,67) ( *, *) ( *, *) *(x=37,lam=rho+ [0,0,0,0], nu= [3,3,3,-3]/2) 3x2x1^4^e 53: 4 [C+,C-,C+,C+] 60 37 66 68 ( *, *) ( *, *) ( *, *) ( *, *) *(x=35,lam=rho+ [0,0,0,0], nu= [1,2,-1,0]/1) 2x1^3^4^e 54: 4 [C+,C-,C+,C+] 61 38 67 69 ( *, *) ( *, *) ( *, *) ( *, *) *(x=35,lam=rho+ [0,-1,0,1], nu= [1,2,-1,0]/1) 2x1^3^4^e 55: 4 [C+,i2,C+,C-] 65 55 65 39 ( *, *) (68,69) ( *, *) ( *, *) *(x=36,lam=rho+ [0,0,0,0], nu= [3,3,3,3]/2) 4x2x1^3^e 56: 5 [C-,C+,C-,C-] 40 70 44 44 ( *, *) ( *, *) ( *, *) ( *, *) *(x=51,lam=rho+ [0,0,0,0], nu= [3,0,1,0]/1) 1x2^3x2x4^e 57: 5 [C-,C+,C-,C-] 41 71 45 45 ( *, *) ( *, *) ( *, *) ( *, *) *(x=51,lam=rho+[-1,0,-1,0], nu= [3,0,1,0]/1) 1x2^3x2x4^e 58: 5 [C-,C+,C-,C-] 42 72 46 46 ( *, *) ( *, *) ( *, *) ( *, *) *(x=52,lam=rho+ [0,0,0,0], nu= [3,0,1,0]/1) 1x2^3x2x4^e 59: 5 [C-,C+,C-,C-] 43 73 47 47 ( *, *) ( *, *) ( *, *) ( *, *) *(x=52,lam=rho+[-1,0,-1,0], nu= [3,0,1,0]/1) 1x2^3x2x4^e 60: 5 [C-,r1,C+,C+] 53 60 74 76 ( *, *) (44,46) ( *, *) ( *, *) *(x=48,lam=rho+ [0,0,0,0], nu= [6,1,-1,0]/2) 1x2x1^3^4^e 61: 5 [C-,r1,C+,C+] 54 61 75 77 ( *, *) (45,47) ( *, *) ( *, *) *(x=48,lam=rho+ [-1,0,0,1], nu= [6,1,-1,0]/2) 1x2x1^3^4^e 62: 5 [C-,C+,C-,C-] 52 78 48 52 ( *, *) ( *, *) ( *, *) ( *, *) *(x=50,lam=rho+ [0,0,0,0], nu= [2,1,2,-1]/1) 1x3x2x1^4^e 63: 5 [i2,C-,i1,i1] 63 49 64 64 (70,71) ( *, *) (78, *) (79, *) *(x=53,lam=rho+ [0,0,0,0], nu= [5,5,0,0]/2) 2x1x3x2x4^e 64: 5 [i2,C-,i1,i1] 64 50 63 63 (72,73) ( *, *) (78, *) (79, *) *(x=54,lam=rho+ [0,0,0,0], nu= [5,5,0,0]/2) 2x1x3x2x4^e 65: 5 [C-,C+,C-,C-] 55 79 55 51 ( *, *) ( *, *) ( *, *) ( *, *) *(x=49,lam=rho+ [0,0,0,0], nu= [2,1,2,1]/1) 1x4x2x1^3^e 66: 5 [C+,r2,C-,C+] 74 67 53 80 ( *, *) (52, *) ( *, *) ( *, *) *(x=47,lam=rho+ [0,0,0,0], nu= [3,4,2,-3]/2) 2^3x2x1^4^e 67: 5 [C+,r2,C-,C+] 75 66 54 81 ( *, *) (52, *) ( *, *) ( *, *) *(x=47,lam=rho+ [0,-1,1,0], nu= [3,4,2,-3]/2) 2^3x2x1^4^e 68: 5 [C+,r2,C+,C-] 76 69 80 53 ( *, *) (55, *) ( *, *) ( *, *) *(x=46,lam=rho+ [0,0,0,0], nu= [3,4,2,3]/2) 2^4x2x1^3^e 69: 5 [C+,r2,C+,C-] 77 68 81 54 ( *, *) (55, *) ( *, *) ( *, *) *(x=46,lam=rho+[0,-1,-1,0], nu= [3,4,2,3]/2) 2^4x2x1^3^e 70: 6 [r2,C-,i1,i1] 71 56 72 72 (63, *) ( *, *) (82, *) (84, *) *(x=60,lam=rho+ [0,0,0,0], nu= [3,2,0,0]/1) 1^2x1x3x2x4^e 71: 6 [r2,C-,i1,i1] 70 57 73 73 (63, *) ( *, *) (83, *) (85, *) *(x=60,lam=rho+[-1,-1,0,0], nu= [3,2,0,0]/1) 1^2x1x3x2x4^e 72: 6 [r2,C-,i1,i1] 73 58 70 70 (64, *) ( *, *) (82, *) (84, *) *(x=61,lam=rho+ [0,0,0,0], nu= [3,2,0,0]/1) 1^2x1x3x2x4^e 73: 6 [r2,C-,i1,i1] 72 59 71 71 (64, *) ( *, *) (83, *) (85, *) *(x=61,lam=rho+[-1,-1,0,0], nu= [3,2,0,0]/1) 1^2x1x3x2x4^e 74: 6 [C-,C+,C-,C+] 66 82 60 86 ( *, *) ( *, *) ( *, *) ( *, *) *(x=57,lam=rho+ [0,0,0,0], nu= [3,1,1,-1]/1) 1x2^3x2x1^4^e 75: 6 [C-,C+,C-,C+] 67 83 61 87 ( *, *) ( *, *) ( *, *) ( *, *) *(x=57,lam=rho+ [-1,0,1,0], nu= [3,1,1,-1]/1) 1x2^3x2x1^4^e 76: 6 [C-,C+,C+,C-] 68 84 86 60 ( *, *) ( *, *) ( *, *) ( *, *) *(x=56,lam=rho+ [0,0,0,0], nu= [3,1,1,1]/1) 1x2^4x2x1^3^e 77: 6 [C-,C+,C+,C-] 69 85 87 61 ( *, *) ( *, *) ( *, *) ( *, *) *(x=56,lam=rho+[-1,0,-1,0], nu= [3,1,1,1]/1) 1x2^4x2x1^3^e 78: 6 [i2,C-,r1,i2] 78 62 78 78 (82,83) ( *, *) (63,64) (88,89) *(x=59,lam=rho+ [0,0,0,0], nu= [5,5,1,-1]/2) 2x1x3x2x1^4^e 79: 6 [i2,C-,i2,r1] 79 65 79 79 (84,85) ( *, *) (88,89) (63,64) *(x=58,lam=rho+ [0,0,0,0], nu= [5,5,1,1]/2) 2x1x4x2x1^3^e 80: 6 [C+,C+,C-,C-] 86 88 68 66 ( *, *) ( *, *) ( *, *) ( *, *) *(x=55,lam=rho+ [0,0,0,0], nu= [2,2,2,0]/1) 3x2^4x2x1^3^e 81: 6 [C+,C+,C-,C-] 87 89 69 67 ( *, *) ( *, *) ( *, *) ( *, *) *(x=55,lam=rho+[0,-1,0,-1], nu= [2,2,2,0]/1) 3x2^4x2x1^3^e 82: 7 [r2,C-,r1,i2] 83 74 82 82 (78, *) ( *, *) (70,72) (90,93) *(x=65,lam=rho+ [0,0,0,0], nu= [6,4,1,-1]/2) 1^2x1x3x2x1^4^e 83: 7 [r2,C-,r1,i2] 82 75 83 83 (78, *) ( *, *) (71,73) (91,94) *(x=65,lam=rho+ [-1,3,0,0], nu= [6,4,1,-1]/2) 1^2x1x3x2x1^4^e 84: 7 [r2,C-,i2,r1] 85 76 84 84 (79, *) ( *, *) (90,93) (70,72) *(x=63,lam=rho+ [0,0,0,0], nu= [6,4,1,1]/2) 1^2x1x4x2x1^3^e 85: 7 [r2,C-,i2,r1] 84 77 85 85 (79, *) ( *, *) (91,94) (71,73) *(x=63,lam=rho+[-1,-1,0,0], nu= [6,4,1,1]/2) 1^2x1x4x2x1^3^e 86: 7 [C-,i2,C-,C-] 80 86 76 74 ( *, *) (90,92) ( *, *) ( *, *) *(x=64,lam=rho+ [0,0,0,0], nu= [6,3,3,0]/2) 1x3x2^4x2x1^3^e 87: 7 [C-,i2,C-,C-] 81 87 77 75 ( *, *) (94,95) ( *, *) ( *, *) *(x=64,lam=rho+[-1,0,0,-1], nu= [6,3,3,0]/2) 1x3x2^4x2x1^3^e 88: 7 [i2,C-,r2,r2] 88 80 89 89 (90,91) ( *, *) (79, *) (78, *) *(x=62,lam=rho+ [0,0,0,0], nu= [5,5,2,0]/2) 2x3x2^4x2x1^3^e 89: 7 [i2,C-,r2,r2] 89 81 88 88 (93,94) ( *, *) (79, *) (78, *) *(x=62,lam=rho+[0,0,-1,-1], nu= [5,5,2,0]/2) 2x3x2^4x2x1^3^e 90: 8 [r2,r2,r2,r2] 91 92 93 93 (88, *) (86, *) (84, *) (82, *) *(x=66,lam=rho+ [0,0,0,0], nu= [3,2,1,0]/1) 1^2x3x2^4x2x1^3^e 91: 8 [r2,rn,r2,r2] 90 91 94 94 (88, *) ( *, *) (85, *) (83, *) *(x=66,lam=rho+[-1,-1,0,0], nu= [3,2,1,0]/1) 1^2x3x2^4x2x1^3^e 92: 8 [rn,r2,rn,rn] 92 90 92 92 ( *, *) (86, *) ( *, *) ( *, *) *(x=66,lam=rho+[0,-1,-1,0], nu= [3,2,1,0]/1) 1^2x3x2^4x2x1^3^e 93: 8 [r2,rn,r2,r2] 94 93 90 90 (89, *) ( *, *) (84, *) (82, *) *(x=66,lam=rho+[0,0,-1,-1], nu= [3,2,1,0]/1) 1^2x3x2^4x2x1^3^e 94: 8 [r2,r2,r2,r2] 93 95 91 91 (89, *) (87, *) (85, *) (83, *) *(x=66,lam=rho+[-1,-1,-1,-1], nu= [3,2,1,0]/1) 1^2x3x2^4x2x1^3^e 95: 8 [rn,r2,rn,rn] 95 94 95 95 ( *, *) (87, *) ( *, *) ( *, *) *(x=66,lam=rho+[-1,0,0,-1], nu= [3,2,1,0]/1) 1^2x3x2^4x2x1^3^e atlas> p Value: final parameter (x=66,lambda=[3,2,1,0]/1,nu=[3,2,1,0]/1) atlas> show(composition_series (I(p))) 1*J(x=0,lambda=[3/1,2/1,1/1,0/1],nu=[0/1,0/1,0/1,0/1]) 3*J(x=1,lambda=[3/1,2/1,1/1,0/1],nu=[0/1,0/1,0/1,0/1]) 2*J(x=2,lambda=[3/1,2/1,1/1,0/1],nu=[0/1,0/1,0/1,0/1]) 3*J(x=3,lambda=[3/1,2/1,1/1,0/1],nu=[0/1,0/1,0/1,0/1]) 1*J(x=4,lambda=[3/1,2/1,1/1,0/1],nu=[0/1,0/1,0/1,0/1]) 2*J(x=5,lambda=[3/1,2/1,1/1,0/1],nu=[0/1,0/1,0/1,0/1]) 2*J(x=6,lambda=[3/1,2/1,1/1,0/1],nu=[0/1,0/1,1/2,1/2]) 2*J(x=7,lambda=[3/1,2/1,1/1,0/1],nu=[0/1,0/1,1/2,1/2]) 1*J(x=8,lambda=[3/1,2/1,1/1,0/1],nu=[0/1,1/2,-1/2,0/1]) 1*J(x=9,lambda=[3/1,2/1,1/1,0/1],nu=[0/1,1/2,-1/2,0/1]) 2*J(x=10,lambda=[3/1,2/1,1/1,0/1],nu=[0/1,0/1,1/2,-1/2]) 2*J(x=11,lambda=[3/1,2/1,1/1,0/1],nu=[0/1,0/1,1/2,-1/2]) 2*J(x=12,lambda=[3/1,2/1,1/1,0/1],nu=[1/2,-1/2,0/1,0/1]) 2*J(x=13,lambda=[3/1,2/1,1/1,0/1],nu=[1/2,-1/2,0/1,0/1]) 2*J(x=14,lambda=[3/1,2/1,1/1,0/1],nu=[0/1,0/1,1/1,0/1]) 1*J(x=14,lambda=[3/1,2/1,2/1,1/1],nu=[0/1,0/1,1/1,0/1]) 2*J(x=15,lambda=[3/1,2/1,1/1,0/1],nu=[0/1,0/1,1/1,0/1]) 1*J(x=15,lambda=[3/1,2/1,2/1,1/1],nu=[0/1,0/1,1/1,0/1]) 3*J(x=16,lambda=[3/1,2/1,1/1,0/1],nu=[1/2,-1/2,1/2,1/2]) 3*J(x=17,lambda=[3/1,2/1,1/1,0/1],nu=[1/2,-1/2,1/2,-1/2]) 3*J(x=18,lambda=[3/1,2/1,1/1,0/1],nu=[0/1,1/1,0/1,1/1]) 3*J(x=19,lambda=[3/1,2/1,1/1,0/1],nu=[0/1,1/1,0/1,1/1]) 3*J(x=20,lambda=[3/1,2/1,1/1,0/1],nu=[0/1,1/1,0/1,-1/1]) 3*J(x=21,lambda=[3/1,2/1,1/1,0/1],nu=[0/1,1/1,0/1,-1/1]) 3*J(x=22,lambda=[3/1,2/1,1/1,0/1],nu=[1/1,0/1,-1/1,0/1]) 3*J(x=23,lambda=[3/1,2/1,1/1,0/1],nu=[1/1,0/1,-1/1,0/1]) 5*J(x=24,lambda=[3/1,2/1,1/1,0/1],nu=[1/2,-1/2,1/1,0/1]) 2*J(x=24,lambda=[3/1,2/1,2/1,-1/1],nu=[1/2,-1/2,1/1,0/1]) 2*J(x=25,lambda=[3/1,2/1,1/1,0/1],nu=[1/1,1/1,-1/1,1/1]) 1*J(x=26,lambda=[3/1,2/1,1/1,0/1],nu=[0/1,2/1,0/1,0/1]) 1*J(x=26,lambda=[3/1,3/1,1/1,1/1],nu=[0/1,2/1,0/1,0/1]) 1*J(x=27,lambda=[3/1,2/1,1/1,0/1],nu=[0/1,2/1,0/1,0/1]) 1*J(x=27,lambda=[3/1,3/1,1/1,1/1],nu=[0/1,2/1,0/1,0/1]) 2*J(x=28,lambda=[3/1,2/1,1/1,0/1],nu=[1/1,1/1,-1/1,-1/1]) 2*J(x=29,lambda=[3/1,2/1,1/1,0/1],nu=[0/1,3/2,3/2,0/1]) 2*J(x=30,lambda=[3/1,2/1,1/1,0/1],nu=[0/1,3/2,3/2,0/1]) 2*J(x=31,lambda=[3/1,2/1,1/1,0/1],nu=[3/2,0/1,0/1,3/2]) 2*J(x=32,lambda=[3/1,2/1,1/1,0/1],nu=[3/2,0/1,0/1,3/2]) 2*J(x=33,lambda=[3/1,2/1,1/1,0/1],nu=[3/2,0/1,0/1,-3/2]) 2*J(x=34,lambda=[3/1,2/1,1/1,0/1],nu=[3/2,0/1,0/1,-3/2]) 2*J(x=35,lambda=[3/1,2/1,1/1,0/1],nu=[1/1,2/1,-1/1,0/1]) 2*J(x=35,lambda=[3/1,3/1,1/1,-1/1],nu=[1/1,2/1,-1/1,0/1]) 1*J(x=36,lambda=[3/1,2/1,1/1,0/1],nu=[3/2,3/2,3/2,3/2]) 1*J(x=37,lambda=[3/1,2/1,1/1,0/1],nu=[3/2,3/2,3/2,-3/2]) 1*J(x=38,lambda=[3/1,2/1,1/1,0/1],nu=[0/1,2/1,1/1,0/1]) 2*J(x=38,lambda=[3/1,3/1,2/1,0/1],nu=[0/1,2/1,1/1,0/1]) 1*J(x=39,lambda=[3/1,2/1,1/1,0/1],nu=[0/1,2/1,1/1,0/1]) 2*J(x=39,lambda=[3/1,3/1,2/1,0/1],nu=[0/1,2/1,1/1,0/1]) 3*J(x=40,lambda=[3/1,2/1,1/1,0/1],nu=[3/2,1/2,-1/2,3/2]) 1*J(x=41,lambda=[3/1,2/1,1/1,0/1],nu=[3/1,0/1,0/1,0/1]) 1*J(x=42,lambda=[3/1,2/1,1/1,0/1],nu=[3/1,0/1,0/1,0/1]) 3*J(x=43,lambda=[3/1,2/1,1/1,0/1],nu=[3/2,1/2,-1/2,-3/2]) 1*J(x=44,lambda=[3/1,2/1,1/1,0/1],nu=[2/1,0/1,2/1,0/1]) 1*J(x=45,lambda=[3/1,2/1,1/1,0/1],nu=[2/1,0/1,2/1,0/1]) 1*J(x=46,lambda=[3/1,2/1,1/1,0/1],nu=[3/2,2/1,1/1,3/2]) 1*J(x=46,lambda=[3/1,3/1,2/1,0/1],nu=[3/2,2/1,1/1,3/2]) 1*J(x=47,lambda=[3/1,2/1,1/1,0/1],nu=[3/2,2/1,1/1,-3/2]) 1*J(x=47,lambda=[3/1,3/1,0/1,0/1],nu=[3/2,2/1,1/1,-3/2]) 2*J(x=48,lambda=[3/1,2/1,1/1,0/1],nu=[3/1,1/2,-1/2,0/1]) 1*J(x=49,lambda=[3/1,2/1,1/1,0/1],nu=[2/1,1/1,2/1,1/1]) 1*J(x=50,lambda=[3/1,2/1,1/1,0/1],nu=[2/1,1/1,2/1,-1/1]) 1*J(x=51,lambda=[3/1,2/1,1/1,0/1],nu=[3/1,0/1,1/1,0/1]) 1*J(x=52,lambda=[3/1,2/1,1/1,0/1],nu=[3/1,0/1,1/1,0/1]) 1*J(x=53,lambda=[3/1,2/1,1/1,0/1],nu=[5/2,5/2,0/1,0/1]) 1*J(x=54,lambda=[3/1,2/1,1/1,0/1],nu=[5/2,5/2,0/1,0/1]) 1*J(x=55,lambda=[3/1,2/1,1/1,0/1],nu=[2/1,2/1,2/1,0/1]) 1*J(x=56,lambda=[3/1,2/1,1/1,0/1],nu=[3/1,1/1,1/1,1/1]) 1*J(x=57,lambda=[3/1,2/1,1/1,0/1],nu=[3/1,1/1,1/1,-1/1]) 1*J(x=58,lambda=[3/1,2/1,1/1,0/1],nu=[5/2,5/2,1/2,1/2]) 1*J(x=59,lambda=[3/1,2/1,1/1,0/1],nu=[5/2,5/2,1/2,-1/2]) 1*J(x=60,lambda=[3/1,2/1,1/1,0/1],nu=[3/1,2/1,0/1,0/1]) 1*J(x=61,lambda=[3/1,2/1,1/1,0/1],nu=[3/1,2/1,0/1,0/1]) 1*J(x=62,lambda=[3/1,2/1,1/1,0/1],nu=[5/2,5/2,1/1,0/1]) 1*J(x=63,lambda=[3/1,2/1,1/1,0/1],nu=[3/1,2/1,1/2,1/2]) 1*J(x=64,lambda=[3/1,2/1,1/1,0/1],nu=[3/1,3/2,3/2,0/1]) 1*J(x=65,lambda=[3/1,2/1,1/1,0/1],nu=[3/1,2/1,1/2,-1/2]) 1*J(x=66,lambda=[3/1,2/1,1/1,0/1],nu=[3/1,2/1,1/1,0/1]) atlas> p Value: final parameter (x=66,lambda=[3,2,1,0]/1,nu=[3,2,1,0]/1) atlas> print_block(p) Parameter defines element 90 of the following block: 0: 0 [i1,i1,i1,i1] 1 2 3 3 (10, *) ( 6, *) (12, *) ( 8, *) *(x= 0,lam=rho+ [0,0,0,0], nu= [0,0,0,0]/1) e 1: 0 [i1,ic,i1,i1] 0 1 4 4 (10, *) ( *, *) (13, *) ( 9, *) *(x= 1,lam=rho+ [0,0,0,0], nu= [0,0,0,0]/1) e 2: 0 [ic,i1,ic,ic] 2 0 2 2 ( *, *) ( 6, *) ( *, *) ( *, *) *(x= 2,lam=rho+ [0,0,0,0], nu= [0,0,0,0]/1) e 3: 0 [i1,ic,i1,i1] 4 3 0 0 (11, *) ( *, *) (12, *) ( 8, *) *(x= 3,lam=rho+ [0,0,0,0], nu= [0,0,0,0]/1) e 4: 0 [i1,i1,i1,i1] 3 5 1 1 (11, *) ( 7, *) (13, *) ( 9, *) *(x= 4,lam=rho+ [0,0,0,0], nu= [0,0,0,0]/1) e 5: 0 [ic,i1,ic,ic] 5 4 5 5 ( *, *) ( 7, *) ( *, *) ( *, *) *(x= 5,lam=rho+ [0,0,0,0], nu= [0,0,0,0]/1) e 6: 1 [C+,r1,C+,C+] 16 6 18 14 ( *, *) ( 0, 2) ( *, *) ( *, *) *(x= 8,lam=rho+ [0,0,0,0], nu= [0,1,-1,0]/2) 2^e 7: 1 [C+,r1,C+,C+] 17 7 19 15 ( *, *) ( 4, 5) ( *, *) ( *, *) *(x= 9,lam=rho+ [0,0,0,0], nu= [0,1,-1,0]/2) 2^e 8: 1 [i1,C+,i2,r1] 9 14 8 8 (20, *) ( *, *) (21,22) ( 0, 3) *(x= 6,lam=rho+ [0,0,0,0], nu= [0,0,1,1]/2) 4^e 9: 1 [i1,C+,i2,r1] 8 15 9 9 (20, *) ( *, *) (23,24) ( 1, 4) *(x= 7,lam=rho+ [0,0,0,0], nu= [0,0,1,1]/2) 4^e 10: 1 [r1,C+,i1,i1] 10 16 11 11 ( 0, 1) ( *, *) (25, *) (20, *) *(x=12,lam=rho+ [0,0,0,0], nu= [1,-1,0,0]/2) 1^e 11: 1 [r1,C+,i1,i1] 11 17 10 10 ( 3, 4) ( *, *) (25, *) (20, *) *(x=13,lam=rho+ [0,0,0,0], nu= [1,-1,0,0]/2) 1^e 12: 1 [i1,C+,r1,i2] 13 18 12 12 (25, *) ( *, *) ( 0, 3) (21,22) *(x=10,lam=rho+ [0,0,0,0], nu= [0,0,1,-1]/2) 3^e 13: 1 [i1,C+,r1,i2] 12 19 13 13 (25, *) ( *, *) ( 1, 4) (23,24) *(x=11,lam=rho+ [0,0,0,0], nu= [0,0,1,-1]/2) 3^e 14: 2 [C+,C-,C+,C-] 30 8 32 6 ( *, *) ( *, *) ( *, *) ( *, *) *(x=18,lam=rho+ [0,0,0,0], nu= [0,1,0,1]/1) 2x4^e 15: 2 [C+,C-,C+,C-] 31 9 33 7 ( *, *) ( *, *) ( *, *) ( *, *) *(x=19,lam=rho+ [0,0,0,0], nu= [0,1,0,1]/1) 2x4^e 16: 2 [C-,C-,C+,C+] 6 10 34 30 ( *, *) ( *, *) ( *, *) ( *, *) *(x=22,lam=rho+ [0,0,0,0], nu= [1,0,-1,0]/1) 1x2^e 17: 2 [C-,C-,C+,C+] 7 11 35 31 ( *, *) ( *, *) ( *, *) ( *, *) *(x=23,lam=rho+ [0,0,0,0], nu= [1,0,-1,0]/1) 1x2^e 18: 2 [C+,C-,C-,C+] 34 12 6 32 ( *, *) ( *, *) ( *, *) ( *, *) *(x=20,lam=rho+ [0,0,0,0], nu= [0,1,0,-1]/1) 2x3^e 19: 2 [C+,C-,C-,C+] 35 13 7 33 ( *, *) ( *, *) ( *, *) ( *, *) *(x=21,lam=rho+ [0,0,0,0], nu= [0,1,0,-1]/1) 2x3^e 20: 2 [r1,C+,i2,r1] 20 36 20 20 ( 8, 9) ( *, *) (37,38) (10,11) *(x=16,lam=rho+ [0,0,0,0], nu= [1,-1,1,1]/2) 1^4^e 21: 2 [i1,C+,r2,r2] 23 26 22 22 (37, *) ( *, *) ( 8, *) (12, *) *(x=14,lam=rho+ [0,0,0,0], nu= [0,0,1,0]/1) 3^4^e 22: 2 [i1,C+,r2,r2] 24 27 21 21 (38, *) ( *, *) ( 8, *) (12, *) *(x=14,lam=rho+[0,0,-1,-3], nu= [0,0,1,0]/1) 3^4^e 23: 2 [i1,C+,r2,r2] 21 28 24 24 (37, *) ( *, *) ( 9, *) (13, *) *(x=15,lam=rho+ [0,0,0,0], nu= [0,0,1,0]/1) 3^4^e 24: 2 [i1,C+,r2,r2] 22 29 23 23 (38, *) ( *, *) ( 9, *) (13, *) *(x=15,lam=rho+[0,0,-1,-3], nu= [0,0,1,0]/1) 3^4^e 25: 2 [r1,C+,r1,i2] 25 39 25 25 (12,13) ( *, *) (10,11) (37,38) *(x=17,lam=rho+ [0,0,0,0], nu=[1,-1,1,-1]/2) 1^3^e 26: 3 [C+,C-,C+,C+] 44 21 40 40 ( *, *) ( *, *) ( *, *) ( *, *) *(x=26,lam=rho+ [0,0,0,0], nu= [0,2,0,0]/1) 2x3^4^e 27: 3 [C+,C-,C+,C+] 45 22 41 41 ( *, *) ( *, *) ( *, *) ( *, *) *(x=26,lam=rho+[0,-1,0,-3], nu= [0,2,0,0]/1) 2x3^4^e 28: 3 [C+,C-,C+,C+] 46 23 42 42 ( *, *) ( *, *) ( *, *) ( *, *) *(x=27,lam=rho+ [0,0,0,0], nu= [0,2,0,0]/1) 2x3^4^e 29: 3 [C+,C-,C+,C+] 47 24 43 43 ( *, *) ( *, *) ( *, *) ( *, *) *(x=27,lam=rho+[0,-1,0,-3], nu= [0,2,0,0]/1) 2x3^4^e 30: 3 [C-,i1,C+,C-] 14 31 49 16 ( *, *) (48, *) ( *, *) ( *, *) *(x=31,lam=rho+ [0,0,0,0], nu= [3,0,0,3]/2) 1x2x4^e 31: 3 [C-,i1,C+,C-] 15 30 50 17 ( *, *) (48, *) ( *, *) ( *, *) *(x=32,lam=rho+ [0,0,0,0], nu= [3,0,0,3]/2) 1x2x4^e 32: 3 [C+,i2,C-,C-] 49 32 14 18 ( *, *) (40,41) ( *, *) ( *, *) *(x=29,lam=rho+ [0,0,0,0], nu= [0,3,3,0]/2) 3x2x4^e 33: 3 [C+,i2,C-,C-] 50 33 15 19 ( *, *) (42,43) ( *, *) ( *, *) *(x=30,lam=rho+ [0,0,0,0], nu= [0,3,3,0]/2) 3x2x4^e 34: 3 [C-,i1,C-,C+] 18 35 16 49 ( *, *) (51, *) ( *, *) ( *, *) *(x=33,lam=rho+ [0,0,0,0], nu= [3,0,0,-3]/2) 1x2x3^e 35: 3 [C-,i1,C-,C+] 19 34 17 50 ( *, *) (51, *) ( *, *) ( *, *) *(x=34,lam=rho+ [0,0,0,0], nu= [3,0,0,-3]/2) 1x2x3^e 36: 3 [C+,C-,C+,C+] 48 20 52 48 ( *, *) ( *, *) ( *, *) ( *, *) *(x=25,lam=rho+ [0,0,0,0], nu= [1,1,-1,1]/1) 2x1^4^e 37: 3 [r1,C+,r2,r2] 37 53 38 38 (21,23) ( *, *) (20, *) (25, *) *(x=24,lam=rho+ [0,0,0,0], nu= [1,-1,2,0]/2) 1^3^4^e 38: 3 [r1,C+,r2,r2] 38 54 37 37 (22,24) ( *, *) (20, *) (25, *) *(x=24,lam=rho+ [0,0,-1,1], nu= [1,-1,2,0]/2) 1^3^4^e 39: 3 [C+,C-,C+,C+] 51 25 51 55 ( *, *) ( *, *) ( *, *) ( *, *) *(x=28,lam=rho+ [0,0,0,0], nu=[1,1,-1,-1]/1) 2x1^3^e 40: 4 [C+,r2,C-,C-] 56 41 26 26 ( *, *) (32, *) ( *, *) ( *, *) *(x=38,lam=rho+ [0,0,0,0], nu= [0,2,1,0]/1) 2^3x2x4^e 41: 4 [C+,r2,C-,C-] 57 40 27 27 ( *, *) (32, *) ( *, *) ( *, *) *(x=38,lam=rho+[0,-1,-1,0], nu= [0,2,1,0]/1) 2^3x2x4^e 42: 4 [C+,r2,C-,C-] 58 43 28 28 ( *, *) (33, *) ( *, *) ( *, *) *(x=39,lam=rho+ [0,0,0,0], nu= [0,2,1,0]/1) 2^3x2x4^e 43: 4 [C+,r2,C-,C-] 59 42 29 29 ( *, *) (33, *) ( *, *) ( *, *) *(x=39,lam=rho+[0,-1,-1,0], nu= [0,2,1,0]/1) 2^3x2x4^e 44: 4 [C-,i1,C+,C+] 26 46 56 56 ( *, *) (60, *) ( *, *) ( *, *) *(x=41,lam=rho+ [0,0,0,0], nu= [3,0,0,0]/1) 1x2x3^4^e 45: 4 [C-,i1,C+,C+] 27 47 57 57 ( *, *) (61, *) ( *, *) ( *, *) *(x=41,lam=rho+[-1,0,0,-3], nu= [3,0,0,0]/1) 1x2x3^4^e 46: 4 [C-,i1,C+,C+] 28 44 58 58 ( *, *) (60, *) ( *, *) ( *, *) *(x=42,lam=rho+ [0,0,0,0], nu= [3,0,0,0]/1) 1x2x3^4^e 47: 4 [C-,i1,C+,C+] 29 45 59 59 ( *, *) (61, *) ( *, *) ( *, *) *(x=42,lam=rho+[-1,0,0,-3], nu= [3,0,0,0]/1) 1x2x3^4^e 48: 4 [C-,r1,C+,C-] 36 48 62 36 ( *, *) (30,31) ( *, *) ( *, *) *(x=40,lam=rho+ [0,0,0,0], nu= [3,1,-1,3]/2) 1x2x1^4^e 49: 4 [C-,C+,C-,C-] 32 63 30 34 ( *, *) ( *, *) ( *, *) ( *, *) *(x=44,lam=rho+ [0,0,0,0], nu= [2,0,2,0]/1) 1x3x2x4^e 50: 4 [C-,C+,C-,C-] 33 64 31 35 ( *, *) ( *, *) ( *, *) ( *, *) *(x=45,lam=rho+ [0,0,0,0], nu= [2,0,2,0]/1) 1x3x2x4^e 51: 4 [C-,r1,C-,C+] 39 51 39 65 ( *, *) (34,35) ( *, *) ( *, *) *(x=43,lam=rho+ [0,0,0,0], nu=[3,1,-1,-3]/2) 1x2x1^3^e 52: 4 [C+,i2,C-,C+] 62 52 36 62 ( *, *) (66,67) ( *, *) ( *, *) *(x=37,lam=rho+ [0,0,0,0], nu= [3,3,3,-3]/2) 3x2x1^4^e 53: 4 [C+,C-,C+,C+] 60 37 66 68 ( *, *) ( *, *) ( *, *) ( *, *) *(x=35,lam=rho+ [0,0,0,0], nu= [1,2,-1,0]/1) 2x1^3^4^e 54: 4 [C+,C-,C+,C+] 61 38 67 69 ( *, *) ( *, *) ( *, *) ( *, *) *(x=35,lam=rho+ [0,-1,0,1], nu= [1,2,-1,0]/1) 2x1^3^4^e 55: 4 [C+,i2,C+,C-] 65 55 65 39 ( *, *) (68,69) ( *, *) ( *, *) *(x=36,lam=rho+ [0,0,0,0], nu= [3,3,3,3]/2) 4x2x1^3^e 56: 5 [C-,C+,C-,C-] 40 70 44 44 ( *, *) ( *, *) ( *, *) ( *, *) *(x=51,lam=rho+ [0,0,0,0], nu= [3,0,1,0]/1) 1x2^3x2x4^e 57: 5 [C-,C+,C-,C-] 41 71 45 45 ( *, *) ( *, *) ( *, *) ( *, *) *(x=51,lam=rho+[-1,0,-1,0], nu= [3,0,1,0]/1) 1x2^3x2x4^e 58: 5 [C-,C+,C-,C-] 42 72 46 46 ( *, *) ( *, *) ( *, *) ( *, *) *(x=52,lam=rho+ [0,0,0,0], nu= [3,0,1,0]/1) 1x2^3x2x4^e 59: 5 [C-,C+,C-,C-] 43 73 47 47 ( *, *) ( *, *) ( *, *) ( *, *) *(x=52,lam=rho+[-1,0,-1,0], nu= [3,0,1,0]/1) 1x2^3x2x4^e 60: 5 [C-,r1,C+,C+] 53 60 74 76 ( *, *) (44,46) ( *, *) ( *, *) *(x=48,lam=rho+ [0,0,0,0], nu= [6,1,-1,0]/2) 1x2x1^3^4^e 61: 5 [C-,r1,C+,C+] 54 61 75 77 ( *, *) (45,47) ( *, *) ( *, *) *(x=48,lam=rho+ [-1,0,0,1], nu= [6,1,-1,0]/2) 1x2x1^3^4^e 62: 5 [C-,C+,C-,C-] 52 78 48 52 ( *, *) ( *, *) ( *, *) ( *, *) *(x=50,lam=rho+ [0,0,0,0], nu= [2,1,2,-1]/1) 1x3x2x1^4^e 63: 5 [i2,C-,i1,i1] 63 49 64 64 (70,71) ( *, *) (78, *) (79, *) *(x=53,lam=rho+ [0,0,0,0], nu= [5,5,0,0]/2) 2x1x3x2x4^e 64: 5 [i2,C-,i1,i1] 64 50 63 63 (72,73) ( *, *) (78, *) (79, *) *(x=54,lam=rho+ [0,0,0,0], nu= [5,5,0,0]/2) 2x1x3x2x4^e 65: 5 [C-,C+,C-,C-] 55 79 55 51 ( *, *) ( *, *) ( *, *) ( *, *) *(x=49,lam=rho+ [0,0,0,0], nu= [2,1,2,1]/1) 1x4x2x1^3^e 66: 5 [C+,r2,C-,C+] 74 67 53 80 ( *, *) (52, *) ( *, *) ( *, *) *(x=47,lam=rho+ [0,0,0,0], nu= [3,4,2,-3]/2) 2^3x2x1^4^e 67: 5 [C+,r2,C-,C+] 75 66 54 81 ( *, *) (52, *) ( *, *) ( *, *) *(x=47,lam=rho+ [0,-1,1,0], nu= [3,4,2,-3]/2) 2^3x2x1^4^e 68: 5 [C+,r2,C+,C-] 76 69 80 53 ( *, *) (55, *) ( *, *) ( *, *) *(x=46,lam=rho+ [0,0,0,0], nu= [3,4,2,3]/2) 2^4x2x1^3^e 69: 5 [C+,r2,C+,C-] 77 68 81 54 ( *, *) (55, *) ( *, *) ( *, *) *(x=46,lam=rho+[0,-1,-1,0], nu= [3,4,2,3]/2) 2^4x2x1^3^e 70: 6 [r2,C-,i1,i1] 71 56 72 72 (63, *) ( *, *) (82, *) (84, *) *(x=60,lam=rho+ [0,0,0,0], nu= [3,2,0,0]/1) 1^2x1x3x2x4^e 71: 6 [r2,C-,i1,i1] 70 57 73 73 (63, *) ( *, *) (83, *) (85, *) *(x=60,lam=rho+[-1,-1,0,0], nu= [3,2,0,0]/1) 1^2x1x3x2x4^e 72: 6 [r2,C-,i1,i1] 73 58 70 70 (64, *) ( *, *) (82, *) (84, *) *(x=61,lam=rho+ [0,0,0,0], nu= [3,2,0,0]/1) 1^2x1x3x2x4^e 73: 6 [r2,C-,i1,i1] 72 59 71 71 (64, *) ( *, *) (83, *) (85, *) *(x=61,lam=rho+[-1,-1,0,0], nu= [3,2,0,0]/1) 1^2x1x3x2x4^e 74: 6 [C-,C+,C-,C+] 66 82 60 86 ( *, *) ( *, *) ( *, *) ( *, *) *(x=57,lam=rho+ [0,0,0,0], nu= [3,1,1,-1]/1) 1x2^3x2x1^4^e 75: 6 [C-,C+,C-,C+] 67 83 61 87 ( *, *) ( *, *) ( *, *) ( *, *) *(x=57,lam=rho+ [-1,0,1,0], nu= [3,1,1,-1]/1) 1x2^3x2x1^4^e 76: 6 [C-,C+,C+,C-] 68 84 86 60 ( *, *) ( *, *) ( *, *) ( *, *) *(x=56,lam=rho+ [0,0,0,0], nu= [3,1,1,1]/1) 1x2^4x2x1^3^e 77: 6 [C-,C+,C+,C-] 69 85 87 61 ( *, *) ( *, *) ( *, *) ( *, *) *(x=56,lam=rho+[-1,0,-1,0], nu= [3,1,1,1]/1) 1x2^4x2x1^3^e 78: 6 [i2,C-,r1,i2] 78 62 78 78 (82,83) ( *, *) (63,64) (88,89) *(x=59,lam=rho+ [0,0,0,0], nu= [5,5,1,-1]/2) 2x1x3x2x1^4^e 79: 6 [i2,C-,i2,r1] 79 65 79 79 (84,85) ( *, *) (88,89) (63,64) *(x=58,lam=rho+ [0,0,0,0], nu= [5,5,1,1]/2) 2x1x4x2x1^3^e 80: 6 [C+,C+,C-,C-] 86 88 68 66 ( *, *) ( *, *) ( *, *) ( *, *) *(x=55,lam=rho+ [0,0,0,0], nu= [2,2,2,0]/1) 3x2^4x2x1^3^e 81: 6 [C+,C+,C-,C-] 87 89 69 67 ( *, *) ( *, *) ( *, *) ( *, *) *(x=55,lam=rho+[0,-1,0,-1], nu= [2,2,2,0]/1) 3x2^4x2x1^3^e 82: 7 [r2,C-,r1,i2] 83 74 82 82 (78, *) ( *, *) (70,72) (90,93) *(x=65,lam=rho+ [0,0,0,0], nu= [6,4,1,-1]/2) 1^2x1x3x2x1^4^e 83: 7 [r2,C-,r1,i2] 82 75 83 83 (78, *) ( *, *) (71,73) (91,94) *(x=65,lam=rho+ [-1,3,0,0], nu= [6,4,1,-1]/2) 1^2x1x3x2x1^4^e 84: 7 [r2,C-,i2,r1] 85 76 84 84 (79, *) ( *, *) (90,93) (70,72) *(x=63,lam=rho+ [0,0,0,0], nu= [6,4,1,1]/2) 1^2x1x4x2x1^3^e 85: 7 [r2,C-,i2,r1] 84 77 85 85 (79, *) ( *, *) (91,94) (71,73) *(x=63,lam=rho+[-1,-1,0,0], nu= [6,4,1,1]/2) 1^2x1x4x2x1^3^e 86: 7 [C-,i2,C-,C-] 80 86 76 74 ( *, *) (90,92) ( *, *) ( *, *) *(x=64,lam=rho+ [0,0,0,0], nu= [6,3,3,0]/2) 1x3x2^4x2x1^3^e 87: 7 [C-,i2,C-,C-] 81 87 77 75 ( *, *) (94,95) ( *, *) ( *, *) *(x=64,lam=rho+[-1,0,0,-1], nu= [6,3,3,0]/2) 1x3x2^4x2x1^3^e 88: 7 [i2,C-,r2,r2] 88 80 89 89 (90,91) ( *, *) (79, *) (78, *) *(x=62,lam=rho+ [0,0,0,0], nu= [5,5,2,0]/2) 2x3x2^4x2x1^3^e 89: 7 [i2,C-,r2,r2] 89 81 88 88 (93,94) ( *, *) (79, *) (78, *) *(x=62,lam=rho+[0,0,-1,-1], nu= [5,5,2,0]/2) 2x3x2^4x2x1^3^e 90: 8 [r2,r2,r2,r2] 91 92 93 93 (88, *) (86, *) (84, *) (82, *) *(x=66,lam=rho+ [0,0,0,0], nu= [3,2,1,0]/1) 1^2x3x2^4x2x1^3^e 91: 8 [r2,rn,r2,r2] 90 91 94 94 (88, *) ( *, *) (85, *) (83, *) *(x=66,lam=rho+[-1,-1,0,0], nu= [3,2,1,0]/1) 1^2x3x2^4x2x1^3^e 92: 8 [rn,r2,rn,rn] 92 90 92 92 ( *, *) (86, *) ( *, *) ( *, *) *(x=66,lam=rho+[0,-1,-1,0], nu= [3,2,1,0]/1) 1^2x3x2^4x2x1^3^e 93: 8 [r2,rn,r2,r2] 94 93 90 90 (89, *) ( *, *) (84, *) (82, *) *(x=66,lam=rho+[0,0,-1,-1], nu= [3,2,1,0]/1) 1^2x3x2^4x2x1^3^e 94: 8 [r2,r2,r2,r2] 93 95 91 91 (89, *) (87, *) (85, *) (83, *) *(x=66,lam=rho+[-1,-1,-1,-1], nu= [3,2,1,0]/1) 1^2x3x2^4x2x1^3^e 95: 8 [rn,r2,rn,rn] 95 94 95 95 ( *, *) (87, *) ( *, *) ( *, *) *(x=66,lam=rho+[-1,0,0,-1], nu= [3,2,1,0]/1) 1^2x3x2^4x2x1^3^e atlas> find(B,p) Value: 90 atlas> rho(G) Value: [ 3, 2, 1, 0 ]/1 atlas> p Value: final parameter (x=66,lambda=[3,2,1,0]/1,nu=[3,2,1,0]/1) atlas> set q=B[94] Identifier q: Param (hiding previous one of type Param) atlas> q Value: final parameter (x=66,lambda=[4,3,2,1]/1,nu=[3,2,1,0]/1) atlas> tau(p) Value: [0,1,2,3] atlas> tau(q) Value: [0,1,2,3] atlas> atlas> atlas> {tau(p)=all simple roots <=> J(p) is finite dimensional} atlas> atlas> atlas> infinitesimal_character (p) Value: [ 3, 2, 1, 0 ]/1 atlas> infinitesimal_character (p)=rho(G) Value: true atlas> infinitesimal_character (q)=rho(G) Value: true atlas> pi- Display all 1215 possibilities? (y or n) atlas> pi0 (G) Value: 2 atlas> G Value: disconnected split real group with Lie algebra 'so(4,4)' atlas> {q=sign representation} atlas> atlas> atlas> atlas> atlas> G:=PSO(4,4) Value: disconnected split real group with Lie algebra 'so(4,4)' atlas> pi0 (G) Value: 4 atlas> atlas> B:=block_of (trivial(G)) atlas> #B Value: 111 atlas> print_block(trivial(G)) Parameter defines element 99 of the following block: 0: 0 [i1,i1,i1,i1] 1 2 1 1 ( 5, *) ( 3, *) ( 6, *) ( 4, *) *(x= 0,lam=rho+ [0,0,0,0], nu= [0,0,0,0]/1) e 1: 0 [i1,ic,i1,i1] 0 1 0 0 ( 5, *) ( *, *) ( 6, *) ( 4, *) *(x= 1,lam=rho+ [0,0,0,0], nu= [0,0,0,0]/1) e 2: 0 [ic,i1,ic,ic] 2 0 2 2 ( *, *) ( 3, *) ( *, *) ( *, *) *(x= 2,lam=rho+ [0,0,0,0], nu= [0,0,0,0]/1) e 3: 1 [C+,r1,C+,C+] 8 3 9 7 ( *, *) ( 0, 2) ( *, *) ( *, *) *(x= 4,lam=rho+ [0,0,0,0], nu= [0,1,0,0]/2) 2^e 4: 1 [i2,C+,i2,r1] 4 7 4 4 ( 10, 11) ( *, *) ( 12, 13) ( 0, 1) *(x= 3,lam=rho+ [0,0,0,0], nu= [0,0,0,1]/2) 4^e 5: 1 [r1,C+,i2,i2] 5 8 5 5 ( 0, 1) ( *, *) ( 14, 15) ( 10, 11) *(x= 6,lam=rho+ [0,0,0,0], nu= [1,0,0,0]/2) 1^e 6: 1 [i2,C+,r1,i2] 6 9 6 6 ( 14, 15) ( *, *) ( 0, 1) ( 12, 13) *(x= 5,lam=rho+ [0,0,0,0], nu= [0,0,1,0]/2) 3^e 7: 2 [C+,C-,C+,C-] 18 4 19 3 ( *, *) ( *, *) ( *, *) ( *, *) *(x=10,lam=rho+ [0,0,0,0], nu= [0,1,0,1]/1) 2x4^e 8: 2 [C-,C-,C+,C+] 3 5 20 18 ( *, *) ( *, *) ( *, *) ( *, *) *(x=12,lam=rho+ [0,0,0,0], nu= [1,1,0,0]/1) 1x2^e 9: 2 [C+,C-,C-,C+] 20 6 3 19 ( *, *) ( *, *) ( *, *) ( *, *) *(x=11,lam=rho+ [0,0,0,0], nu= [0,1,1,0]/1) 2x3^e 10: 2 [r2,C+,i2,r2] 11 21 10 11 ( 4, *) ( *, *) ( 23, 25) ( 5, *) *(x= 8,lam=rho+ [0,0,0,0], nu= [1,0,0,1]/2) 1^4^e 11: 2 [r2,C+,i2,r2] 10 22 11 10 ( 4, *) ( *, *) ( 24, 26) ( 5, *) *(x= 8,lam=rho+ [0,0,0,-1], nu= [1,0,0,1]/2) 1^4^e 12: 2 [i2,C+,r2,r2] 12 16 13 13 ( 23, 26) ( *, *) ( 4, *) ( 6, *) *(x= 7,lam=rho+ [0,0,0,0], nu= [0,0,1,1]/2) 3^4^e 13: 2 [i2,C+,r2,r2] 13 17 12 12 ( 24, 25) ( *, *) ( 4, *) ( 6, *) *(x= 7,lam=rho+ [0,0,0,3], nu= [0,0,1,1]/2) 3^4^e 14: 2 [r2,C+,r2,i2] 15 27 15 14 ( 6, *) ( *, *) ( 5, *) ( 23, 24) *(x= 9,lam=rho+ [0,0,0,0], nu= [1,0,1,0]/2) 1^3^e 15: 2 [r2,C+,r2,i2] 14 28 14 15 ( 6, *) ( *, *) ( 5, *) ( 25, 26) *(x= 9,lam=rho+ [0,0,-1,0], nu= [1,0,1,0]/2) 1^3^e 16: 3 [C+,C-,C+,C+] 31 12 29 29 ( *, *) ( *, *) ( *, *) ( *, *) *(x=15,lam=rho+ [0,0,0,0], nu= [0,2,1,1]/1) 2x3^4^e 17: 3 [C+,C-,C+,C+] 32 13 30 30 ( *, *) ( *, *) ( *, *) ( *, *) *(x=15,lam=rho+ [0,3,0,3], nu= [0,2,1,1]/1) 2x3^4^e 18: 3 [C-,i2,C+,C-] 7 18 35 8 ( *, *) ( 33, 34) ( *, *) ( *, *) *(x=18,lam=rho+ [0,0,0,0], nu= [3,3,0,3]/2) 1x2x4^e 19: 3 [C+,i2,C-,C-] 35 19 7 9 ( *, *) ( 29, 30) ( *, *) ( *, *) *(x=17,lam=rho+ [0,0,0,0], nu= [0,3,3,3]/2) 3x2x4^e 20: 3 [C-,i2,C-,C+] 9 20 8 35 ( *, *) ( 36, 37) ( *, *) ( *, *) *(x=19,lam=rho+ [0,0,0,0], nu= [3,3,3,0]/2) 1x2x3^e 21: 3 [C+,C-,C+,C+] 33 10 38 33 ( *, *) ( *, *) ( *, *) ( *, *) *(x=14,lam=rho+ [0,0,0,0], nu= [1,2,0,1]/1) 2x1^4^e 22: 3 [C+,C-,C+,C+] 34 11 39 34 ( *, *) ( *, *) ( *, *) ( *, *) *(x=14,lam=rho+[0,-1,0,-1], nu= [1,2,0,1]/1) 2x1^4^e 23: 3 [r2,C+,r2,r2] 26 40 25 24 ( 12, *) ( *, *) ( 10, *) ( 14, *) *(x=13,lam=rho+ [0,0,0,0], nu= [1,0,1,1]/2) 1^3^4^e 24: 3 [r2,C+,r2,r2] 25 41 26 23 ( 13, *) ( *, *) ( 11, *) ( 14, *) *(x=13,lam=rho+ [3,0,-3,0], nu= [1,0,1,1]/2) 1^3^4^e 25: 3 [r2,C+,r2,r2] 24 42 23 26 ( 13, *) ( *, *) ( 10, *) ( 15, *) *(x=13,lam=rho+ [3,0,0,-3], nu= [1,0,1,1]/2) 1^3^4^e 26: 3 [r2,C+,r2,r2] 23 43 24 25 ( 12, *) ( *, *) ( 11, *) ( 15, *) *(x=13,lam=rho+ [2,0,1,-3], nu= [1,0,1,1]/2) 1^3^4^e 27: 3 [C+,C-,C+,C+] 36 14 36 44 ( *, *) ( *, *) ( *, *) ( *, *) *(x=16,lam=rho+ [0,0,0,0], nu= [1,2,1,0]/1) 2x1^3^e 28: 3 [C+,C-,C+,C+] 37 15 37 45 ( *, *) ( *, *) ( *, *) ( *, *) *(x=16,lam=rho+[0,-1,-1,0], nu= [1,2,1,0]/1) 2x1^3^e 29: 4 [C+,r2,C-,C-] 46 30 16 16 ( *, *) ( 19, *) ( *, *) ( *, *) *(x=23,lam=rho+ [0,0,0,0], nu= [0,4,3,3]/2) 2^3x2x4^e 30: 4 [C+,r2,C-,C-] 47 29 17 17 ( *, *) ( 19, *) ( *, *) ( *, *) *(x=23,lam=rho+ [0,1,1,1], nu= [0,4,3,3]/2) 2^3x2x4^e 31: 4 [C-,i2,C+,C+] 16 31 46 46 ( *, *) ( 48, 51) ( *, *) ( *, *) *(x=25,lam=rho+ [0,0,0,0], nu= [6,6,3,3]/2) 1x2x3^4^e 32: 4 [C-,i2,C+,C+] 17 32 47 47 ( *, *) ( 49, 50) ( *, *) ( *, *) *(x=25,lam=rho+ [3,3,0,3], nu= [6,6,3,3]/2) 1x2x3^4^e 33: 4 [C-,r2,C+,C-] 21 34 52 21 ( *, *) ( 18, *) ( *, *) ( *, *) *(x=24,lam=rho+ [0,0,0,0], nu= [3,4,0,3]/2) 1x2x1^4^e 34: 4 [C-,r2,C+,C-] 22 33 53 22 ( *, *) ( 18, *) ( *, *) ( *, *) *(x=24,lam=rho+[-1,-1,0,-1], nu= [3,4,0,3]/2) 1x2x1^4^e 35: 4 [C-,C+,C-,C-] 19 54 18 20 ( *, *) ( *, *) ( *, *) ( *, *) *(x=27,lam=rho+ [0,0,0,0], nu= [2,2,2,2]/1) 1x3x2x4^e 36: 4 [C-,r2,C-,C+] 27 37 27 55 ( *, *) ( 20, *) ( *, *) ( *, *) *(x=26,lam=rho+ [0,0,0,0], nu= [3,4,3,0]/2) 1x2x1^3^e 37: 4 [C-,r2,C-,C+] 28 36 28 56 ( *, *) ( 20, *) ( *, *) ( *, *) *(x=26,lam=rho+[-1,-1,-1,0], nu= [3,4,3,0]/2) 1x2x1^3^e 38: 4 [C+,i2,C-,C+] 52 38 21 52 ( *, *) ( 57, 59) ( *, *) ( *, *) *(x=22,lam=rho+ [0,0,0,0], nu= [3,6,6,3]/2) 3x2x1^4^e 39: 4 [C+,i2,C-,C+] 53 39 22 53 ( *, *) ( 58, 60) ( *, *) ( *, *) *(x=22,lam=rho+[0,-1,-1,-1], nu= [3,6,6,3]/2) 3x2x1^4^e 40: 4 [C+,C-,C+,C+] 48 23 57 61 ( *, *) ( *, *) ( *, *) ( *, *) *(x=20,lam=rho+ [0,0,0,0], nu= [1,3,1,1]/1) 2x1^3^4^e 41: 4 [C+,C-,C+,C+] 49 24 58 62 ( *, *) ( *, *) ( *, *) ( *, *) *(x=20,lam=rho+ [3,0,-3,0], nu= [1,3,1,1]/1) 2x1^3^4^e 42: 4 [C+,C-,C+,C+] 50 25 59 63 ( *, *) ( *, *) ( *, *) ( *, *) *(x=20,lam=rho+ [3,0,0,-3], nu= [1,3,1,1]/1) 2x1^3^4^e 43: 4 [C+,C-,C+,C+] 51 26 60 64 ( *, *) ( *, *) ( *, *) ( *, *) *(x=20,lam=rho+ [2,0,1,-3], nu= [1,3,1,1]/1) 2x1^3^4^e 44: 4 [C+,i2,C+,C-] 55 44 55 27 ( *, *) ( 61, 62) ( *, *) ( *, *) *(x=21,lam=rho+ [0,0,0,0], nu= [3,6,3,6]/2) 4x2x1^3^e 45: 4 [C+,i2,C+,C-] 56 45 56 28 ( *, *) ( 63, 64) ( *, *) ( *, *) *(x=21,lam=rho+[0,-1,-1,-1], nu= [3,6,3,6]/2) 4x2x1^3^e 46: 5 [C-,C+,C-,C-] 29 65 31 31 ( *, *) ( *, *) ( *, *) ( *, *) *(x=33,lam=rho+ [0,0,0,0], nu= [3,3,2,2]/1) 1x2^3x2x4^e 47: 5 [C-,C+,C-,C-] 30 66 32 32 ( *, *) ( *, *) ( *, *) ( *, *) *(x=33,lam=rho+ [1,1,1,1], nu= [3,3,2,2]/1) 1x2^3x2x4^e 48: 5 [C-,r2,C+,C+] 40 51 67 71 ( *, *) ( 31, *) ( *, *) ( *, *) *(x=30,lam=rho+ [0,0,0,0], nu= [6,7,3,3]/2) 1x2x1^3^4^e 49: 5 [C-,r2,C+,C+] 41 50 68 72 ( *, *) ( 32, *) ( *, *) ( *, *) *(x=30,lam=rho+[-3,0,-3,0], nu= [6,7,3,3]/2) 1x2x1^3^4^e 50: 5 [C-,r2,C+,C+] 42 49 69 73 ( *, *) ( 32, *) ( *, *) ( *, *) *(x=30,lam=rho+[-3,0,0,-3], nu= [6,7,3,3]/2) 1x2x1^3^4^e 51: 5 [C-,r2,C+,C+] 43 48 70 74 ( *, *) ( 31, *) ( *, *) ( *, *) *(x=30,lam=rho+[-2,0,1,-3], nu= [6,7,3,3]/2) 1x2x1^3^4^e 52: 5 [C-,C+,C-,C-] 38 75 33 38 ( *, *) ( *, *) ( *, *) ( *, *) *(x=32,lam=rho+ [0,0,0,0], nu= [2,3,3,2]/1) 1x3x2x1^4^e 53: 5 [C-,C+,C-,C-] 39 76 34 39 ( *, *) ( *, *) ( *, *) ( *, *) *(x=32,lam=rho+[-1,-1,-1,-1], nu= [2,3,3,2]/1) 1x3x2x1^4^e 54: 5 [i2,C-,i2,i2] 54 35 54 54 ( 65, 66) ( *, *) ( 75, 76) ( 77, 78) *(x=34,lam=rho+ [0,0,0,0], nu= [5,10,5,5]/2) 2x1x3x2x4^e 55: 5 [C-,C+,C-,C-] 44 77 44 36 ( *, *) ( *, *) ( *, *) ( *, *) *(x=31,lam=rho+ [0,0,0,0], nu= [2,3,2,3]/1) 1x4x2x1^3^e 56: 5 [C-,C+,C-,C-] 45 78 45 37 ( *, *) ( *, *) ( *, *) ( *, *) *(x=31,lam=rho+[-1,-1,-1,-1], nu= [2,3,2,3]/1) 1x4x2x1^3^e 57: 5 [C+,r2,C-,C+] 67 59 40 79 ( *, *) ( 38, *) ( *, *) ( *, *) *(x=29,lam=rho+ [0,0,0,0], nu= [3,7,6,3]/2) 2^3x2x1^4^e 58: 5 [C+,r2,C-,C+] 68 60 41 80 ( *, *) ( 39, *) ( *, *) ( *, *) *(x=29,lam=rho+ [3,0,3,0], nu= [3,7,6,3]/2) 2^3x2x1^4^e 59: 5 [C+,r2,C-,C+] 69 57 42 81 ( *, *) ( 38, *) ( *, *) ( *, *) *(x=29,lam=rho+ [3,0,0,-3], nu= [3,7,6,3]/2) 2^3x2x1^4^e 60: 5 [C+,r2,C-,C+] 70 58 43 82 ( *, *) ( 39, *) ( *, *) ( *, *) *(x=29,lam=rho+[2,0,-1,-3], nu= [3,7,6,3]/2) 2^3x2x1^4^e 61: 5 [C+,r2,C+,C-] 71 62 79 40 ( *, *) ( 44, *) ( *, *) ( *, *) *(x=28,lam=rho+ [0,0,0,0], nu= [3,7,3,6]/2) 2^4x2x1^3^e 62: 5 [C+,r2,C+,C-] 72 61 80 41 ( *, *) ( 44, *) ( *, *) ( *, *) *(x=28,lam=rho+ [3,0,-3,0], nu= [3,7,3,6]/2) 2^4x2x1^3^e 63: 5 [C+,r2,C+,C-] 73 64 81 42 ( *, *) ( 45, *) ( *, *) ( *, *) *(x=28,lam=rho+ [3,0,0,3], nu= [3,7,3,6]/2) 2^4x2x1^3^e 64: 5 [C+,r2,C+,C-] 74 63 82 43 ( *, *) ( 45, *) ( *, *) ( *, *) *(x=28,lam=rho+ [2,0,1,3], nu= [3,7,3,6]/2) 2^4x2x1^3^e 65: 6 [r2,C-,i2,i2] 66 46 65 65 ( 54, *) ( *, *) ( 83, 85) ( 87, 89) *(x=40,lam=rho+ [0,0,0,0], nu= [6,10,5,5]/2) 1^2x1x3x2x4^e 66: 6 [r2,C-,i2,i2] 65 47 66 66 ( 54, *) ( *, *) ( 84, 86) ( 88, 90) *(x=40,lam=rho+ [1,2,1,1], nu= [6,10,5,5]/2) 1^2x1x3x2x4^e 67: 6 [C-,C+,C-,C+] 57 83 48 91 ( *, *) ( *, *) ( *, *) ( *, *) *(x=37,lam=rho+ [0,0,0,0], nu= [3,4,3,2]/1) 1x2^3x2x1^4^e 68: 6 [C-,C+,C-,C+] 58 86 49 92 ( *, *) ( *, *) ( *, *) ( *, *) *(x=37,lam=rho+ [-3,0,3,0], nu= [3,4,3,2]/1) 1x2^3x2x1^4^e 69: 6 [C-,C+,C-,C+] 59 84 50 93 ( *, *) ( *, *) ( *, *) ( *, *) *(x=37,lam=rho+[-3,0,0,-3], nu= [3,4,3,2]/1) 1x2^3x2x1^4^e 70: 6 [C-,C+,C-,C+] 60 85 51 94 ( *, *) ( *, *) ( *, *) ( *, *) *(x=37,lam=rho+[-2,0,-1,-3], nu= [3,4,3,2]/1) 1x2^3x2x1^4^e 71: 6 [C-,C+,C+,C-] 61 87 91 48 ( *, *) ( *, *) ( *, *) ( *, *) *(x=36,lam=rho+ [0,0,0,0], nu= [3,4,2,3]/1) 1x2^4x2x1^3^e 72: 6 [C-,C+,C+,C-] 62 88 92 49 ( *, *) ( *, *) ( *, *) ( *, *) *(x=36,lam=rho+[-3,0,-3,0], nu= [3,4,2,3]/1) 1x2^4x2x1^3^e 73: 6 [C-,C+,C+,C-] 63 90 93 50 ( *, *) ( *, *) ( *, *) ( *, *) *(x=36,lam=rho+ [-3,0,0,3], nu= [3,4,2,3]/1) 1x2^4x2x1^3^e 74: 6 [C-,C+,C+,C-] 64 89 94 51 ( *, *) ( *, *) ( *, *) ( *, *) *(x=36,lam=rho+ [-2,0,1,3], nu= [3,4,2,3]/1) 1x2^4x2x1^3^e 75: 6 [i2,C-,r2,i2] 75 52 76 75 ( 83, 84) ( *, *) ( 54, *) ( 95, 97) *(x=39,lam=rho+ [0,0,0,0], nu= [5,10,6,5]/2) 2x1x3x2x1^4^e 76: 6 [i2,C-,r2,i2] 76 53 75 76 ( 85, 86) ( *, *) ( 54, *) ( 96, 98) *(x=39,lam=rho+[-1,-2,-1,-1], nu= [5,10,6,5]/2) 2x1x3x2x1^4^e 77: 6 [i2,C-,i2,r2] 77 55 77 78 ( 87, 88) ( *, *) ( 95, 96) ( 54, *) *(x=38,lam=rho+ [0,0,0,0], nu= [5,10,5,6]/2) 2x1x4x2x1^3^e 78: 6 [i2,C-,i2,r2] 78 56 78 77 ( 89, 90) ( *, *) ( 97, 98) ( 54, *) *(x=38,lam=rho+[-1,-2,-1,-1], nu= [5,10,5,6]/2) 2x1x4x2x1^3^e 79: 6 [C+,C+,C-,C-] 91 95 61 57 ( *, *) ( *, *) ( *, *) ( *, *) *(x=35,lam=rho+ [0,0,0,0], nu= [2,4,3,3]/1) 3x2^4x2x1^3^e 80: 6 [C+,C+,C-,C-] 92 96 62 58 ( *, *) ( *, *) ( *, *) ( *, *) *(x=35,lam=rho+ [3,0,3,0], nu= [2,4,3,3]/1) 3x2^4x2x1^3^e 81: 6 [C+,C+,C-,C-] 93 97 63 59 ( *, *) ( *, *) ( *, *) ( *, *) *(x=35,lam=rho+ [3,0,0,3], nu= [2,4,3,3]/1) 3x2^4x2x1^3^e 82: 6 [C+,C+,C-,C-] 94 98 64 60 ( *, *) ( *, *) ( *, *) ( *, *) *(x=35,lam=rho+ [2,0,-1,3], nu= [2,4,3,3]/1) 3x2^4x2x1^3^e 83: 7 [r2,C-,r2,i2] 84 67 85 83 ( 75, *) ( *, *) ( 65, *) ( 99,103) *(x=44,lam=rho+ [0,0,0,0], nu= [6,10,6,5]/2) 1^2x1x3x2x1^4^e 84: 7 [r2,C-,r2,i2] 83 69 86 84 ( 75, *) ( *, *) ( 66, *) (100,105) *(x=44,lam=rho+[-3,-6,0,-3], nu= [6,10,6,5]/2) 1^2x1x3x2x1^4^e 85: 7 [r2,C-,r2,i2] 86 70 83 85 ( 76, *) ( *, *) ( 65, *) (102,106) *(x=44,lam=rho+[-2,-6,-1,-3], nu= [6,10,6,5]/2) 1^2x1x3x2x1^4^e 86: 7 [r2,C-,r2,i2] 85 68 84 86 ( 76, *) ( *, *) ( 66, *) (104,108) *(x=44,lam=rho+[-1,-4,-1,-2], nu= [6,10,6,5]/2) 1^2x1x3x2x1^4^e 87: 7 [r2,C-,i2,r2] 88 71 87 89 ( 77, *) ( *, *) ( 99,102) ( 65, *) *(x=42,lam=rho+ [0,0,0,0], nu= [6,10,5,6]/2) 1^2x1x4x2x1^3^e 88: 7 [r2,C-,i2,r2] 87 72 88 90 ( 77, *) ( *, *) (100,104) ( 66, *) *(x=42,lam=rho+[-3,-6,-3,0], nu= [6,10,5,6]/2) 1^2x1x4x2x1^3^e 89: 7 [r2,C-,i2,r2] 90 74 89 87 ( 78, *) ( *, *) (103,106) ( 65, *) *(x=42,lam=rho+ [-2,2,1,3], nu= [6,10,5,6]/2) 1^2x1x4x2x1^3^e 90: 7 [r2,C-,i2,r2] 89 73 90 88 ( 78, *) ( *, *) (105,108) ( 66, *) *(x=42,lam=rho+ [-1,4,2,3], nu= [6,10,5,6]/2) 1^2x1x4x2x1^3^e 91: 7 [C-,i2,C-,C-] 79 91 71 67 ( *, *) ( 99,101) ( *, *) ( *, *) *(x=43,lam=rho+ [0,0,0,0], nu= [6,9,6,6]/2) 1x3x2^4x2x1^3^e 92: 7 [C-,i2,C-,C-] 80 92 72 68 ( *, *) (104,107) ( *, *) ( *, *) *(x=43,lam=rho+ [-3,0,3,0], nu= [6,9,6,6]/2) 1x3x2^4x2x1^3^e 93: 7 [C-,i2,C-,C-] 81 93 73 69 ( *, *) (105,109) ( *, *) ( *, *) *(x=43,lam=rho+ [-3,0,0,3], nu= [6,9,6,6]/2) 1x3x2^4x2x1^3^e 94: 7 [C-,i2,C-,C-] 82 94 74 70 ( *, *) (106,110) ( *, *) ( *, *) *(x=43,lam=rho+[-2,0,-1,3], nu= [6,9,6,6]/2) 1x3x2^4x2x1^3^e 95: 7 [i2,C-,r2,r2] 95 79 96 97 ( 99,100) ( *, *) ( 77, *) ( 75, *) *(x=41,lam=rho+ [0,0,0,0], nu= [5,10,6,6]/2) 2x3x2^4x2x1^3^e 96: 7 [i2,C-,r2,r2] 96 80 95 98 (102,104) ( *, *) ( 77, *) ( 76, *) *(x=41,lam=rho+ [3,6,3,0], nu= [5,10,6,6]/2) 2x3x2^4x2x1^3^e 97: 7 [i2,C-,r2,r2] 97 81 98 95 (103,105) ( *, *) ( 78, *) ( 75, *) *(x=41,lam=rho+ [3,6,0,3], nu= [5,10,6,6]/2) 2x3x2^4x2x1^3^e 98: 7 [i2,C-,r2,r2] 98 82 97 96 (106,108) ( *, *) ( 78, *) ( 76, *) *(x=41,lam=rho+ [2,4,-1,3], nu= [5,10,6,6]/2) 2x3x2^4x2x1^3^e 99: 8 [r2,r2,r2,r2] 100 101 102 103 ( 95, *) ( 91, *) ( 87, *) ( 83, *) *(x=45,lam=rho+ [0,0,0,0], nu= [3,5,3,3]/1) 1^2x3x2^4x2x1^3^e 100: 8 [r2,rn,r2,r2] 99 100 104 105 ( 95, *) ( *, *) ( 88, *) ( 84, *) *(x=45,lam=rho+ [-1,0,0,0], nu= [3,5,3,3]/1) 1^2x3x2^4x2x1^3^e 101: 8 [rn,r2,rn,rn] 101 99 101 101 ( *, *) ( 91, *) ( *, *) ( *, *) *(x=45,lam=rho+ [0,-1,0,0], nu= [3,5,3,3]/1) 1^2x3x2^4x2x1^3^e 102: 8 [r2,rn,r2,r2] 104 102 99 106 ( 96, *) ( *, *) ( 87, *) ( 85, *) *(x=45,lam=rho+ [0,0,-1,0], nu= [3,5,3,3]/1) 1^2x3x2^4x2x1^3^e 103: 8 [r2,rn,r2,r2] 105 103 106 99 ( 97, *) ( *, *) ( 89, *) ( 83, *) *(x=45,lam=rho+ [0,0,0,-1], nu= [3,5,3,3]/1) 1^2x3x2^4x2x1^3^e 104: 8 [r2,r2,r2,r2] 102 107 100 108 ( 96, *) ( 92, *) ( 88, *) ( 86, *) *(x=45,lam=rho+[-1,0,-1,0], nu= [3,5,3,3]/1) 1^2x3x2^4x2x1^3^e 105: 8 [r2,r2,r2,r2] 103 109 108 100 ( 97, *) ( 93, *) ( 90, *) ( 84, *) *(x=45,lam=rho+[-1,0,0,-1], nu= [3,5,3,3]/1) 1^2x3x2^4x2x1^3^e 106: 8 [r2,r2,r2,r2] 108 110 103 102 ( 98, *) ( 94, *) ( 89, *) ( 85, *) *(x=45,lam=rho+[0,0,-1,-1], nu= [3,5,3,3]/1) 1^2x3x2^4x2x1^3^e 107: 8 [rn,r2,rn,rn] 107 104 107 107 ( *, *) ( 92, *) ( *, *) ( *, *) *(x=45,lam=rho+[-1,-1,-1,0], nu= [3,5,3,3]/1) 1^2x3x2^4x2x1^3^e 108: 8 [r2,rn,r2,r2] 106 108 105 104 ( 98, *) ( *, *) ( 90, *) ( 86, *) *(x=45,lam=rho+[-1,0,-1,-1], nu= [3,5,3,3]/1) 1^2x3x2^4x2x1^3^e 109: 8 [rn,r2,rn,rn] 109 105 109 109 ( *, *) ( 93, *) ( *, *) ( *, *) *(x=45,lam=rho+[-1,-1,0,-1], nu= [3,5,3,3]/1) 1^2x3x2^4x2x1^3^e 110: 8 [rn,r2,rn,rn] 110 106 110 110 ( *, *) ( 94, *) ( *, *) ( *, *) *(x=45,lam=rho+[0,-1,-1,-1], nu= [3,5,3,3]/1) 1^2x3x2^4x2x1^3^e atlas> {4 one-dimensionals J(99,104,105,106} atlas> atlas> atlas> block_sizes (G) Value: | 0, 0, 0, 0, 1 | | 0, 6, 0, 0, 28 | | 0, 0, 6, 0, 28 | | 0, 0, 0, 6, 28 | | 1, 38, 38, 38, 111 | atlas> block_sizes (PSO(4,4)) Value: | 0, 0, 0, 0, 1 | | 0, 6, 0, 0, 28 | | 0, 0, 6, 0, 28 | | 0, 0, 0, 6, 28 | | 1, 38, 38, 38, 111 | atlas> block_sizes (SO(4,4)) Value: | 0, 0, 0, 0, 1 | | 0, 6, 0, 0, 28 | | 0, 0, 6, 0, 38 | | 0, 0, 0, 6, 38 | | 1, 28, 38, 38, 96 | atlas> block_sizes (Spin(4,4)) Value: | 0, 0, 0, 0, 1 | | 0, 6, 0, 0, 38 | | 0, 0, 6, 0, 38 | | 0, 0, 0, 6, 38 | | 1, 28, 28, 28, 111 | atlas> {Vogan duality! representations of PSO(4,4) are dual to those of Spin(4,4)} atlas> atlas> atlas> G:=Sp(8,R) Value: connected split real group with Lie algebra 'sp(8,R)' atlas> block_sizes (G) Value: | 0, 0, 0, 0, 1 | | 0, 0, 0, 0, 16 | | 0, 0, 0, 0, 42 | | 1, 9, 48, 144, 258 | atlas> atlas> atlas> print_real_forms (G) 0: sp(4) 1: sp(3,1) 2: sp(2,2) 3: sp(8,R) atlas> print_real_forms (dual_quasisplit_form (G)) 0: so(9) 1: so(8,1) 2: so(7,2) 3: so(6,3) 4: so(5,4) atlas> block_sizes (PSO(5,4)) Value: | 0, 0, 0, 1 | | 0, 0, 0, 9 | | 0, 0, 0, 48 | | 0, 0, 0, 144 | | 1, 16, 42, 258 | atlas> atlas> atlas> atlas> G Value: connected split real group with Lie algebra 'sp(8,R)' atlas> atlas> atlas> atlas> atlas> set Gd=dual_quasisplit_form (G) Identifier Gd: RealForm atlas> Gd Value: disconnected split real group with Lie algebra 'so(5,4)' atlas> is_adjoint (Gd) Value: true