Unipotent/Stability computation at Thu Dec 4 12:51:32 2008 Unipotent representations for G=G2(split) G6v=G^v=G2(split) Atlas version 0.3./Build date: Nov 19 2007 at 06:09:46. Special Special Orbit Cells Diagram #R A Dual Orbit Cells Diagram #R A G2 0 22 1 1 0 3 00 1 1 Parameters: 0* 0(0,9): 0 0 [i1,i1] 1 2 ( 3, *) ( 4, *) e Dual Parameters: 9* 9(9,0): 4 3 [r2,r2] 10 11 ( 7, *) ( 8, *) 1,2,1,2,1,2 Everything is stable Dimension of space of stable characters: 1 ---------------------------------------------------------------------------- Special Special Orbit Cells Diagram #R A Dual Orbit Cells Diagram #R A G2(a1) 1,2 02 2 S3 G2(a1) 1,2 20 2 S3 Parameters: 2,3,5,7*,10* 2(2,9): 0 0 [ic,i1] 2 0 ( *, *) ( 4, *) e 3(3,7): 1 1 [r1,C+] 3 6 ( 0, 1) ( *, *) 1 5(5,5): 2 2 [C-,C+] 4 8 ( *, *) ( *, *) 1,2,1 7(7,3): 3 1 [C-,i2] 6 7 ( *, *) ( 9,11) 1,2,1,2,1 10(9,1): 4 3 [r2,rn] 9 10 ( 8, *) ( *, *) 2,1,2,1,2,1 Dual Parameters: 11,7,5,3*,1* 11(9,2): 4 3 [rn,r2] 11 9 ( *, *) ( 8, *) 1,2,1,2,1,2 7(7,3): 3 2 [i2,C-] 7 6 ( 9,10) ( *, *) 2,1,2,1,2 5(5,5): 2 1 [C+,C-] 8 4 ( *, *) ( *, *) 2,1,2 3(3,7): 1 2 [C+,r1] 6 3 ( *, *) ( 0, 2) 2 1(1,9): 0 0 [i1,ic] 0 1 ( 4, *) ( *, *) e Dimension of space of stable characters: 4 Basis of stable characters as sums of irreducibles: 2+10* 2+7* 5 -2+3 Basis of stable characters as matrix of coefficients: 1,0,0,0,1 1,0,0,1,0 0,0,1,0,0 -1,1,0,0,0 All combinations of cells with non-zero stable sums Cells Dimension of space of stable sums 2 1 1 2 2,1 4 ---------------------------------------------------------------------------- Special Special Orbit Cells Diagram #R A Dual Orbit Cells Diagram #R A 0 3 00 1 1 G2 0 22 1 1 Parameters: 9* 9(9,0): 4 3 [r2,r2] 10 11 ( 8, *) ( 7, *) 2,1,2,1,2,1 Dual Parameters: 0* 0(0,9): 0 0 [i1,i1] 1 2 ( 4, *) ( 3, *) e Dimension of space of stable characters: 1 Basis of stable characters as sums of irreducibles: 9* Basis of stable characters as matrix of coefficients: 1 ----------------------------------------------------------------------------