Unipotent representations for G = E7, simply connected, hermitian G^v = E7, adjoint, split Atlas version 0.3./Build date: Nov 19 2007 at 06:09:46. Unipotent representations computed from file orbitsAndCells_E7_sc_s_1_3 at Thu Dec 4 10:44:43 2008 O^v diagram(O^v) O cell Unipotent representations E7 2222222 1 15 3016 E7(a1) 2220222 A1 14 2988 16 2989 E7(a2) 2220202 2A1 9 2366 13 2365 12 2973 E6 2022020 (3A1)'' 1975 1967 11 2950 10 2949 E7(a3) 2002022 A2 8 2852 E6(a1) 2002020 A2+A1 7 2643 6 2644 D5 2020020 (A3+A1)'' 1193 1191 3 2225 4 2224 D4 2020000 A5'' 6 33 Number of orbits: 11 Number of even orbits: 8 Number of cells: 19 Number of unipotent representations: 19 All unipotent parameters/duals: Unipotent Dual 6 2967 33 2994 1191 1814 1193 1816 1967 1040 1975 1048 2224 791 2225 792 2365 650 2366 651 2643 372 2644 373 2852 164 2949 66 2950 67 2973 43 2988 27 2989 28 3016 0 Unipotent representations from block file: 6( 6,13329): 0 0 [ic,i1,ic,i1,i1,i1,i1] 6 54 6 17 43 18 41 ( *, *) ( 122, *) ( *, *) ( 93, *) ( 91, *) ( 68, *) ( 66, *) e 33( 33,13329): 0 0 [ic,i1,ic,i1,i1,i1,i1] 33 34 33 35 36 37 38 ( *, *) ( 127, *) ( *, *) ( 102, *) ( 87, *) ( 75, *) ( 59, *) e 1191(1191,12536): 8 1 [ic,i1,C-,i1,C+,C-,C+] 1191 1202 1016 1192 1397 1001 1404 ( *, *) (1308, *) ( *, *) (1277, *) ( *, *) ( *, *) ( *, *) 3,1,4,2,3,4,5,6,5,4,2,3,1,4,3 1193(1193,12536): 8 1 [ic,i1,C-,i1,C+,C-,C+] 1193 1194 1015 1200 1389 1006 1410 ( *, *) (1307, *) ( *, *) (1278, *) ( *, *) ( *, *) ( *, *) 3,1,4,2,3,4,5,6,5,4,2,3,1,4,3 1967(1967,10969): 12 1 [ic,C+,ic,C-,C+,C-,i1] 1967 2153 1967 1797 2144 1779 1966 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) (2017, *) 4,3,1,6,5,4,2,3,4,5,6,7,6,5,4,2,3,1,4,3,5,4,6 1975(1975,10969): 12 1 [ic,C+,ic,C-,C+,C-,i1] 1975 2149 1975 1789 2139 1774 1970 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) (2016, *) 4,3,1,6,5,4,2,3,4,5,6,7,6,5,4,2,3,1,4,3,5,4,6 2224(2224, 9864): 14 2 [ic,i1,C-,C+,C+,ic,C+] 2224 2225 2095 2364 2361 2224 2361 ( *, *) (2322, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 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 2225(2225, 9864): 14 2 [ic,i1,C-,C+,C+,ic,C+] 2225 2224 2094 2363 2362 2225 2362 ( *, *) (2322, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 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 2365(2365, 9216): 15 2 [ic,C-,ic,C+,C-,C+,r1] 2365 2185 2365 2472 2227 2498 2365 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) (2300,2307) 2,5,4,3,1,6,5,4,2,3,4,5,6,7,6,5,4,2,3,1,4,3,5,4,2,6,5,7 2366(2366, 9216): 15 2 [ic,C-,ic,C+,C-,C+,r1] 2366 2184 2366 2471 2226 2497 2366 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) (2301,2308) 2,5,4,3,1,6,5,4,2,3,4,5,6,7,6,5,4,2,3,1,4,3,5,4,2,6,5,7 2643(2643, 7798): 17 2 [C-,C+,C+,C-,C+,C-,C+] 2484 2759 2718 2540 2737 2525 2741 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 1,4,3,1,5,4,2,6,5,4,2,3,1,4,3,5,4,2,6,5,7,6,5,4,2,3,1,4,3,5,4,6 2644(2644, 7798): 17 2 [C-,C+,C+,C-,C+,C-,C+] 2483 2760 2717 2539 2738 2526 2742 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 1,4,3,1,5,4,2,6,5,4,2,3,1,4,3,5,4,2,6,5,7,6,5,4,2,3,1,4,3,5,4,6 2852(2852, 5684): 20 3 [C-,C+,C+,C-,C+,ic,ic] 2772 2909 2909 2787 2906 2852 2852 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 1,3,4,2,3,1,4,3,5,4,3,1,6,5,4,2,3,4,5,6,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1 2949(2949, 4201): 22 2 [ic,C+,ic,ic,C+,C-,i1] 2949 2984 2949 2949 2984 2911 2950 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) (2969, *) 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 2950(2950, 4201): 22 2 [ic,C+,ic,ic,C+,C-,i1] 2950 2985 2950 2950 2985 2910 2949 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) (2969, *) 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 2973(2973, 3650): 23 3 [ic,C-,ic,C+,C-,C+,C-] 2973 2938 2973 2990 2943 2993 2942 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 2,5,4,2,3,1,4,3,5,4,2,6,5,4,2,3,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,4,5,6,7 2988(2988, 3543): 23 2 [C-,C-,C-,C+,ic,ic,C-] 2960 2964 2965 3002 2988 2988 2967 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 1,2,3,1,4,2,3,5,4,2,3,1,6,5,4,2,3,1,4,5,6,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3 2989(2989, 3543): 23 2 [C-,C-,C-,C+,ic,ic,C-] 2959 2963 2966 3003 2989 2989 2968 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 1,2,3,1,4,2,3,5,4,2,3,1,6,5,4,2,3,1,4,5,6,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3 3016(3016, 1488): 27 3 [C-,ic,ic,ic,ic,C-,r1] 3012 3016 3016 3016 3016 3013 3016 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) (3014,3015) 1,3,4,2,5,4,3,1,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,4,5,6,7 Dual to unipotent representations from dual block: 2967(13329, 6): 35 9 [rn,r2,rn,r2,r2,r2,r2] 2967 3015 2967 2978 3004 2979 3002 ( *, *) (2895, *) ( *, *) (2914, *) (2936, *) (2937, *) (2959, *) 1,2,3,1,4,2,3,1,4,3,5,4,2,3,1,4,3,5,4,2,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,4,5,6,7 2994(13329, 33): 35 9 [rn,r2,rn,r2,r2,r2,r2] 2994 2995 2994 2996 2997 2998 2999 ( *, *) (2900, *) ( *, *) (2923, *) (2932, *) (2944, *) (2952, *) 1,2,3,1,4,2,3,1,4,3,5,4,2,3,1,4,3,5,4,2,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,4,5,6,7 1814(12536,1191): 27 8 [rn,r2,C+,r2,C-,C+,C-] 1814 1825 2001 1815 1624 2010 1607 ( *, *) (1709, *) ( *, *) (1738, *) ( *, *) ( *, *) ( *, *) 1,2,4,2,5,4,2,3,1,4,3,5,4,6,5,4,2,3,1,4,3,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,4,5,6,7 1816(12536,1193): 27 8 [rn,r2,C+,r2,C-,C+,C-] 1816 1817 2000 1823 1616 2015 1613 ( *, *) (1708, *) ( *, *) (1739, *) ( *, *) ( *, *) ( *, *) 1,2,4,2,5,4,2,3,1,4,3,5,4,6,5,4,2,3,1,4,3,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,4,5,6,7 1040(10969,1967): 23 8 [rn,C-,rn,C+,C-,C+,r2] 1040 862 1040 1230 877 1236 1039 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) (1000, *) 1,2,3,1,4,3,1,5,4,2,3,1,4,3,5,4,2,6,5,4,2,3,4,5,6,7,6,5,4,2,3,1,4,3,5,4,2,6,5,7 1048(10969,1975): 23 8 [rn,C-,rn,C+,C-,C+,r2] 1048 858 1048 1222 872 1231 1043 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( 999, *) 1,2,3,1,4,3,1,5,4,2,3,1,4,3,5,4,2,6,5,4,2,3,4,5,6,7,6,5,4,2,3,1,4,3,5,4,2,6,5,7 791( 9864,2224): 21 7 [rn,r2,C+,C-,C-,rn,C-] 791 792 922 653 654 791 654 ( *, *) ( 694, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 1,2,4,2,5,4,2,3,1,6,5,4,2,3,1,4,3,5,6,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,7,6,5 792( 9864,2225): 21 7 [rn,r2,C+,C-,C-,rn,C-] 792 791 921 652 655 792 655 ( *, *) ( 694, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 1,2,4,2,5,4,2,3,1,6,5,4,2,3,1,4,3,5,6,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,7,6,5 650( 9216,2365): 20 7 [rn,C+,rn,C-,C+,C-,i2] 650 832 650 545 790 519 650 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( 705, 712) 1,3,1,4,2,3,1,4,3,5,4,2,3,4,5,6,5,4,2,3,4,5,6,7,6,5,4,2,3,1,4,3,5,4,6 651( 9216,2366): 20 7 [rn,C+,rn,C-,C+,C-,i2] 651 831 651 544 789 518 651 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( 706, 713) 1,3,1,4,2,3,1,4,3,5,4,2,3,4,5,6,5,4,2,3,4,5,6,7,6,5,4,2,3,1,4,3,5,4,6 372( 7798,2643): 18 7 [C+,C-,C-,C+,C-,C+,C-] 535 256 299 477 278 490 276 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 2,3,1,4,3,1,5,4,2,3,1,4,3,6,5,4,7,6,5,4,2,3,1,4,3,5,4,2,6,5,7 373( 7798,2644): 18 7 [C+,C-,C-,C+,C-,C+,C-] 534 257 298 476 279 491 277 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 2,3,1,4,3,1,5,4,2,3,1,4,3,6,5,4,7,6,5,4,2,3,1,4,3,5,4,2,6,5,7 164( 5684,2852): 15 5 [C+,C-,C-,C+,C-,rn,rn] 244 107 107 229 110 164 164 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 2,3,5,4,2,3,4,5,6,5,4,2,3,4,5,6,7,6,5,4,2,3,4,5,6,7 66( 4201,2949): 13 7 [rn,C-,rn,rn,C-,C+,r2] 66 31 66 66 31 106 67 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( 47, *) 1,2,3,1,4,2,3,1,4,3,5,4,2,3,1,4,3,5,4,2,7 67( 4201,2950): 13 7 [rn,C-,rn,rn,C-,C+,r2] 67 32 67 67 32 105 66 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( 47, *) 1,2,3,1,4,2,3,1,4,3,5,4,2,3,1,4,3,5,4,2,7 43( 3650,2973): 12 5 [rn,C+,rn,C-,C+,C-,C+] 43 78 43 26 73 23 74 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 1,3,1,4,2,3,1,4,3,6,5,4,2,3,1,4,3,5,4,6 27( 3543,2988): 12 7 [C+,C+,C+,C-,rn,rn,C+] 57 53 50 13 27 27 48 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 4,2,3,5,4,2,3,4,6,5,4,2,3,4,5,7,6,5,4 28( 3543,2989): 12 7 [C+,C+,C+,C-,rn,rn,C+] 56 52 51 14 28 28 49 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 4,2,3,5,4,2,3,4,6,5,4,2,3,4,5,7,6,5,4 0( 1488,3016): 8 5 [C+,rn,rn,rn,rn,C+,i2] 4 0 0 0 0 3 0 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( 1, 2) 2,3,4,2,3,4,5,4,2,3,4,5