Unipotent representations for G = E7, simply connected, quaternionic 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_2_3 at Thu Dec 4 10:43:48 2008 O^v diagram(O^v) O cell Unipotent representations E7 2222222 1 31 9575 E7(a1) 2220222 A1 30 9564 E7(a2) 2220202 2A1 28 9381 29 9558 E7(a3) 2002022 A2 18 4890,7017 27 9523,9524 26 9373,9508 E6(a1) 2002020 A2+A1 25 9268 E7(a4) 2002002 A2+2A1 24 9117 23 8775 E7(a5) 0002002 D4(a1) 9 5350,7161 19 5340,7985,9312 20 8873,9231 D5(a1)+A1 2000200 A3+A2 15 8699 A5'' 2000022 D4 3 3328 8 8766 A4 2000020 D5(a1) 6 5479 A3+A2+A1 0000200 A4+A2 12 7924 (A3+A1)'' 2000002 D5 2 1437 4 5483 A2+3A1 0200000 A6 10 5035 (3A1)'' 0000002 E6 0 33 Number of orbits: 20 Number of even orbits: 14 Number of cells: 22 Number of unipotent representations: 29 All unipotent parameters/duals: Unipotent Dual 33 9546 1437 8143 3328 6236 4890 4684 5035 4542 5340 4232 5350 4226 5479 4099 5483 4095 7017 2557 7161 2414 7924 1649 7985 1590 8699 876 8766 806 8775 799 8873 702 9117 458 9231 344 9268 307 9312 265 9373 202 9381 194 9508 67 9523 52 9524 53 9558 17 9564 11 9575 2 Unipotent representations from block file: 33( 33,13329): 0 0 [i1,i1,i1,i1,i1,i1,ic] 62 25 27 39 30 41 33 ( 161, *) ( 152, *) ( 135, *) ( 121, *) ( 104, *) ( 94, *) ( *, *) e 1437(1437,12959): 6 1 [C-,C+,i1,i1,i1,i1,C-] 1031 1855 1436 1433 1435 1427 1069 ( *, *) ( *, *) (1734, *) (1724, *) (1713, *) (1708, *) ( *, *) 1,3,4,5,6,7,6,5,4,3,1 3328(3314,11876): 10 1 [C-,i1,C+,i1,i1,C-,ic] 2761 3330 3870 3332 3337 2814 3328 ( *, *) (3791, *) ( *, *) (3734, *) (3727, *) ( *, *) ( *, *) 1,6,5,4,2,3,4,5,6,7,6,5,4,2,3,1,4,5,6 4890(4824,10447): 13 2 [r1,C+,C+,C-,C+,C-,ic] 4890 5519 5511 4349 5459 4325 4890 (4423,4425) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 1,4,3,1,6,5,4,2,3,4,5,6,7,6,5,4,2,3,1,4,3,5,4,6 5035(4951,10210): 14 4 [rn,C-,C+,rn,C+,rn,C+] 5035 4457 5573 5035 5593 5035 5598 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 1,2,4,2,3,1,5,4,2,3,4,5,6,5,4,2,3,1,4,3,5,4,2,6 5340(5246, 9877): 14 2 [i1,C+,C+,C-,i1,C+,C-] 5341 5962 5915 4866 5341 5892 4760 (5758, *) ( *, *) ( *, *) ( *, *) (5624, *) ( *, *) ( *, *) 4,2,3,1,5,4,2,3,1,4,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,7 5350(5256, 9875): 14 2 [C+,C+,i1,C-,C+,C+,C-] 6002 5968 5348 4870 5888 5896 4771 ( *, *) ( *, *) (5660, *) ( *, *) ( *, *) ( *, *) ( *, *) 4,2,3,1,4,5,4,2,3,4,5,6,5,4,3,7,6,5,4,2,3,1,4,3,5,4 5479(5385, 9843): 14 2 [C-,i1,C+,i1,C+,C-,C+] 4777 5478 6038 5476 6008 4907 6012 ( *, *) (5834, *) ( *, *) (5774, *) ( *, *) ( *, *) ( *, *) 1,3,4,2,6,5,4,2,3,1,4,3,5,4,2,6,7,6,5,4,2,3,1,4,5,6 5483(5389, 9842): 14 2 [C-,i1,C+,i1,C+,C+,C-] 4782 5482 6044 5480 6044 6012 4901 ( *, *) (5836, *) ( *, *) (5775, *) ( *, *) ( *, *) ( *, *) 1,3,4,2,5,4,3,1,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7 7017(6813, 7797): 17 2 [C-,C+,C+,C-,C+,ic,ic] 6431 7504 7418 6578 7460 7017 7017 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 1,4,2,3,1,5,4,3,1,6,5,4,2,3,4,5,6,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4 7161(6913, 7323): 18 3 [C+,C+,C+,C-,C+,C+,ic] 7711 7658 7614 6749 7658 7598 7161 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 4,2,3,4,5,4,2,3,1,4,6,5,4,2,3,4,5,6,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4 7924(7622, 6074): 20 4 [C+,rn,C+,C+,C-,C+,C+] 8304 7924 8282 8258 7536 8304 8282 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 2,5,4,2,3,1,4,3,6,5,4,2,3,1,4,3,5,4,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,7,6,5 7985(7647, 5818): 20 3 [C+,C+,C+,C-,C+,i2,C-] 8415 8369 8340 7677 8326 7985 7596 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) (8259,8260) ( *, *) 4,2,3,1,5,4,2,3,1,6,5,4,2,3,1,4,5,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,7,6,5,4 8699(8273, 4271): 22 3 [C-,C+,C+,C+,C-,C+,C+] 8333 8961 8942 8931 8430 8942 8931 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 1,3,4,5,4,2,3,1,4,3,6,5,4,2,3,1,4,3,5,4,6,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5 8766(8340, 4201): 22 2 [ic,C+,i1,i1,C+,C-,ic] 8766 9003 8769 8768 9003 8500 8766 ( *, *) ( *, *) (8874, *) (8867, *) ( *, *) ( *, *) ( *, *) 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 8775(8349, 4199): 22 2 [ic,i1,C+,C-,C+,i1,C-] 8775 8774 8996 8528 8989 8774 8504 ( *, *) (8899, *) ( *, *) ( *, *) ( *, *) (8872, *) ( *, *) 4,2,3,1,4,3,5,4,2,3,1,6,5,4,2,3,1,4,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,4 8873(8407, 3669): 23 3 [C+,C+,C+,C-,C+,C+,C-] 9117 9095 9081 8680 9072 9074 8627 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 4,2,3,1,4,3,5,4,2,3,1,4,6,5,4,2,3,1,4,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,4 9117(8613, 2990): 24 3 [C-,C+,C+,C-,C+,C+,C-] 8873 9281 9241 8978 9261 9263 8930 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 1,4,2,3,1,4,3,5,4,2,3,1,4,5,6,5,4,2,3,1,4,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,4 9231(8695, 2462): 25 3 [C+,C+,i2,C-,C+,C+,C-] 9375 9362 9231 9107 9350 9362 9073 ( *, *) ( *, *) (9310,9311) ( *, *) ( *, *) ( *, *) ( *, *) 4,2,3,1,4,3,5,4,2,3,1,4,3,6,5,4,2,3,1,4,3,5,4,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,4 9268(8732, 2423): 25 3 [C-,C+,C+,C-,C+,C-,C+] 9079 9393 9383 9153 9378 9123 9380 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 1,3,4,2,3,1,4,5,4,2,3,1,4,6,5,4,2,3,1,4,3,5,4,2,6,5,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4 9312(8772, 2122): 26 4 [C+,C+,rn,C-,C+,C+,C-] 9420 9413 9312 9202 9404 9413 9181 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 3,4,2,3,1,4,3,5,4,2,3,1,4,3,6,5,4,2,3,1,4,3,5,4,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,4 9373(8809, 1926): 26 3 [C-,C+,C+,C-,C+,C-,ic] 9229 9462 9440 9292 9451 9261 9373 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 1,4,2,3,1,5,4,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,4,5,6 9381(8817, 1917): 26 3 [C-,ic,r1,C+,C-,C+,C-] 9237 9381 9381 9458 9276 9456 9271 ( *, *) ( *, *) (9304,9306) ( *, *) ( *, *) ( *, *) ( *, *) 1,3,1,4,2,5,4,2,3,1,4,3,5,4,2,6,5,4,2,3,1,4,5,6,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,4,5 9508(8904, 1111): 28 3 [C-,C+,C+,C-,C+,C-,ic] 9437 9544 9538 9464 9544 9452 9508 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 1,4,2,3,4,5,4,2,3,1,4,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,4,5,6 9523(8916, 845): 29 4 [C-,C+,C+,C-,C+,C-,ic] 9472 9556 9550 9487 9556 9480 9523 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 1,3,4,2,3,4,5,4,2,3,1,4,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,4,5,6 9524(8916, 846): 29 4 [C-,C+,C+,C-,C+,C-,ic] 9474 9554 9548 9489 9554 9479 9524 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 1,3,4,2,3,4,5,4,2,3,1,4,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,4,5,6 9558(8935, 557): 30 4 [r2,C-,C-,C+,C-,C+,C-] 9559 9527 9529 9565 9535 9569 9532 (9541, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 1,2,3,1,4,2,3,4,5,4,2,3,1,4,3,5,4,2,6,5,4,2,3,1,4,3,5,4,2,6,5,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,4,5 9564(8940, 548): 30 3 [C-,C-,C-,C+,C-,C-,ic] 9540 9543 9545 9572 9547 9546 9564 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 1,2,3,1,4,2,3,5,4,2,3,1,4,3,5,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,4,5,6 9575(8945, 214): 32 4 [r2,ic,r2,C-,ic,C-,ic] 9574 9575 9573 9569 9575 9565 9575 (9571, *) ( *, *) (9572, *) ( *, *) ( *, *) ( *, *) ( *, *) 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 Dual to unipotent representations from dual block: 9546(13329, 33): 35 9 [r2,r2,r2,r2,r2,r2,rn] 9575 9538 9540 9552 9543 9554 9546 (9403, *) (9426, *) (9441, *) (9459, *) (9474, *) (9496, *) ( *, *) 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 8143(12959,1437): 29 8 [C+,C-,r2,r2,r2,r2,C+] 8555 7707 8142 8139 8141 8133 8497 ( *, *) ( *, *) (7838, *) (7852, *) (7865, *) (7868, *) ( *, *) 2,3,4,2,3,1,4,5,4,2,3,1,4,3,5,4,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,7,6,5,4,2 6236(11876,3314): 25 8 [C+,r2,C-,r2,r2,C+,rn] 6813 6238 5716 6240 6245 6770 6236 ( *, *) (5785, *) ( *, *) (5840, *) (5849, *) ( *, *) ( *, *) 2,3,1,4,2,3,1,4,3,5,4,2,3,1,4,3,5,4,2,6,5,4,2,3,4,5,6,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,7 4684(10447,4824): 22 7 [i2,C-,C-,C+,C-,C+,rn] 4684 4059 4067 5225 4119 5249 4684 (5151,5153) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 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 4542(10210,4951): 21 4 [ic,C+,C-,ic,C-,ic,C-] 4542 5116 4002 4542 3980 4542 3979 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 3,1,4,3,5,4,3,1,6,5,4,3,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,4,5,6,7 4232( 9877,5246): 21 7 [r2,C-,C-,C+,r2,C-,C+] 4233 3612 3661 4708 4233 3686 4818 (3817, *) ( *, *) ( *, *) ( *, *) (3951, *) ( *, *) ( *, *) 1,2,3,1,4,3,5,4,2,3,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,1,4,3,5,6 4226( 9875,5256): 21 7 [C-,C-,r2,C+,C-,C-,C+] 3572 3610 4224 4704 3690 3682 4805 ( *, *) ( *, *) (3916, *) ( *, *) ( *, *) ( *, *) ( *, *) 1,2,3,1,4,5,4,3,1,6,5,4,2,3,1,4,3,5,4,2,6,7,6,5,4,2,3,1,4,3,5,4,2,6,5,7,6 4099( 9843,5385): 21 7 [C+,r2,C-,r2,C-,C+,C-] 4795 4098 3536 4096 3570 4669 3566 ( *, *) (3741, *) ( *, *) (3797, *) ( *, *) ( *, *) ( *, *) 2,3,4,2,3,4,5,4,2,3,1,4,3,5,4,2,6,5,4,3,7,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,7 4095( 9842,5389): 21 7 [C+,r2,C-,r2,C-,C-,C+] 4792 4094 3534 4092 3534 3566 4671 ( *, *) (3740, *) ( *, *) (3796, *) ( *, *) ( *, *) ( *, *) 2,3,4,2,3,4,5,4,2,3,4,5,6,5,4,2,3,1,4,3,5,4,2,6,5,4,3,1,7,6,5,4,2,3,4,5,6 2557( 7797,6813): 18 7 [C+,C-,C-,C+,C-,rn,rn] 3141 2074 2156 2996 2114 2557 2557 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 2,3,1,4,3,5,4,2,3,4,5,6,5,4,2,3,4,5,6,7,6,5,4,2,3,1,4,3,5,6,7 2414( 7323,6913): 17 6 [C-,C-,C-,C+,C-,C-,rn] 1864 1917 1961 2826 1917 1977 2414 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 1,2,3,1,4,2,5,4,2,3,6,5,4,2,3,4,5,6,7,6,5,4,2,3,1,4,3,5,6,7 1649( 6074,7622): 15 4 [C-,ic,C-,C-,C+,C-,C-] 1269 1649 1295 1319 2039 1269 1295 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 1,3,1,4,2,3,1,4,3,5,4,2,6,5,4,2,3,1,7,6,5,4,2,3,1,4,3 1590( 5818,7647): 15 6 [C-,C-,C-,C+,C-,r1,C+] 1160 1206 1235 1898 1249 1590 1979 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) (1314,1315) ( *, *) 1,2,3,1,4,3,5,4,2,3,4,6,5,4,2,3,1,4,5,7,6,5,4,2,3,1 876( 4271,8273): 13 6 [C+,C-,C-,C-,C+,C-,C-] 1242 614 633 644 1145 633 644 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 2,3,4,2,3,1,4,5,4,2,6,5,4,2,3,7,6,5,4,2,3,4 806( 4201,8340): 13 7 [rn,C-,r2,r2,C-,C+,rn] 806 575 809 808 575 1078 806 ( *, *) ( *, *) ( 701, *) ( 708, *) ( *, *) ( *, *) ( *, *) 1,2,3,1,4,2,3,1,4,3,5,4,2,3,1,4,3,5,4,2,7 799( 4199,8349): 13 7 [rn,r2,C-,C+,C-,r2,C+] 799 798 576 1050 585 798 1074 ( *, *) ( 676, *) ( *, *) ( *, *) ( *, *) ( 703, *) ( *, *) 1,2,3,1,5,4,2,3,4,6,5,4,2,3,1,4,3,5,7,6,5 702( 3669,8407): 12 6 [C-,C-,C-,C+,C-,C-,C+] 458 480 494 895 503 501 948 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 1,2,3,1,5,4,2,3,6,5,4,2,3,1,4,3,5,7,6,5 458( 2990,8613): 11 6 [C+,C-,C-,C+,C-,C-,C+] 702 294 334 597 314 312 645 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 2,3,1,5,4,3,6,5,4,2,3,1,4,3,5,7,6,5 344( 2462,8695): 10 6 [C-,C-,r1,C+,C-,C-,C+] 200 213 344 468 225 213 502 ( *, *) ( *, *) ( 263, 264) ( *, *) ( *, *) ( *, *) ( *, *) 1,2,3,1,5,4,2,6,5,4,2,3,1,7,6,5 307( 2423,8732): 10 6 [C+,C-,C-,C+,C-,C+,C-] 496 182 192 422 197 452 195 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 2,3,4,5,4,2,3,6,5,4,7,6,5,4,2,3 265( 2122,8772): 9 4 [C-,C-,ic,C+,C-,C-,C+] 155 160 265 375 169 160 396 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 1,2,3,5,4,2,6,5,4,2,3,1,7,6,5 202( 1926,8809): 9 6 [C+,C-,C-,C+,C-,C+,rn] 346 113 135 283 124 314 202 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 2,3,1,4,3,5,4,2,3,1,4,3,5,7 194( 1917,8817): 9 6 [C+,rn,i2,C-,C+,C-,C+] 338 194 194 117 299 119 304 ( *, *) ( *, *) ( 270, 272) ( *, *) ( *, *) ( *, *) ( *, *) 2,4,2,3,4,6,5,4,2,3,4,5,7,6 67( 1111,8904): 7 6 [C+,C-,C-,C+,C-,C+,rn] 138 31 37 111 31 123 67 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 2,3,1,4,2,5,4,2,3,7 52( 845,8916): 6 4 [C+,C-,C-,C+,C-,C+,rn] 101 21 27 86 21 97 52 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 2,3,4,2,5,4,2,3,7 53( 846,8916): 6 4 [C+,C-,C-,C+,C-,C+,rn] 103 19 25 88 19 96 53 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 2,3,4,2,5,4,2,3,7 17( 557,8935): 5 4 [i1,C+,C+,C-,C+,C-,C+] 18 50 46 8 40 6 43 ( 34, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 4,2,6,5,4,7,6 11( 548,8940): 5 6 [C+,C+,C+,C-,C+,C+,rn] 35 32 30 3 28 29 11 ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) ( *, *) 4,2,3,5,4,7 2( 214,8945): 3 4 [i1,rn,i1,C+,rn,C+,rn] 1 2 0 6 2 8 2 ( 4, *) ( *, *) ( 3, *) ( *, *) ( *, *) ( *, *) ( *, *) 2,5,7