G = E7, adjoint, hermitian G^v = E7, simply connected, split type: E7 ad s real form: 1 dual real form: 3 Dynkin Diagram: 2 | 1-3-4-5-6-7 Infinitesimal character of block: rho Special Special Orbit Cells Diagram #R A DualOrbit Cells Diagram #R A 1 15,16 0000000 1 1 E7 0,1 2222222 2 1 A1 14 1000000 (2) 1 E7(a1) 2 2220222 2 2/1 2A1 10,12,13 0000010 3 1 E7(a2) 3,4,5 2220202 2 1 A2 11 2000000 1 2/2 E7(a3) 7 2002022 4 2/2 A3 5 2000010 (2) 1 D6(a1) 11 2110102 2 1 2A2 6,7 0000020 1 1 D5+A1 9,10 2110110 2 1 A4 1 2000020 1 2/2 D5(a1) 13 2001010 3 2/2 Fundamental weights lambda_2,lambda_5,lambda_7 are not in root lattice Infinitesimal character of block = rho => allowed infinitesimal characters: #0s on 2,5,7 is even not allowed: (3A1)'' 4,9 0000002 (4) 1 E6 6,14 2022020 1 1 A2+A1 8 1000010 (2) 2/2 E6(a1) 8 2002020 2 2/2 (A3+A1)'' 2,3 2000002 (4) 1 D5 12,15 2020020 1 1 A5'' 0 2000022 (2) 1 D4 16 2020000 1 1