Unipotent representations for G = E7, adjoint, hermitian G^v = E7, simply connected, quaternionic Atlas version 0.3./Build date: Nov 19 2007 at 06:09:46. Unipotent representations computed from file orbitsAndCells_E7_ad_s_1_2 at Thu Dec 4 10:44:45 2008 Note: E7, simply connected, quaternionic has two strong real forms There are *two* unipotent representations (at the same infinitesimal character) for each entry in this table. O^v diagram(O^v) O cell Unipotent representations E6 2022020 (3A1)'' 2 293 D5 2020020 (A3+A1)'' 1 156 D4 2020000 A5'' 0 0 Number of orbits: 3 Number of even orbits: 3 Number of cells: 3 Number of unipotent representations: 3 All unipotent parameters/duals: Unipotent Dual 0 314 156 158 293 21 Unipotent representations from block file: 0( 121,8945): 3 3 [ic,rn,ic,C+,rn,C+,rn] 0 0 0 1 0 2 0 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 2,5,7 156(1239,7629): 15 3 [ic,rn,C-,C+,C+,ic,C+] 156 156 142 175 179 156 179 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 2,3,1,4,2,3,4,5,4,2,3,4,6,5,4,2,3,4,7,6,5,4,2,3,1,4,3 293(1631,3871): 23 3 [ic,C+,ic,ic,C+,C-,rn] 293 305 293 293 305 282 293 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,4,5,6,7 Dual to unipotent representations from dual block: 314(8945, 121): 32 4 [rn,ic,rn,C-,ic,C-,ic] 314 314 314 313 314 312 314 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 1,3,1,4,2,3,1,4,3,5,4,2,3,1,4,3,5,4,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,4,5,6 158(7629,1239): 20 4 [rn,ic,C+,C-,C-,rn,C-] 158 158 172 139 135 158 135 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 1,4,2,5,4,2,3,1,6,5,4,2,3,1,4,3,5,6,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,7,6,5 21(3871,1631): 12 4 [rn,C-,rn,rn,C-,C+,ic] 21 9 21 21 9 32 21 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 1,2,3,1,4,2,3,1,4,3,5,4,2,3,1,4,3,5,4,2