Unipotent Packets for big block of SO(4,3) G=SO(4,3) G^v=Sp(6) special special dual orbit cells dual orbit cells #O_R lambda 7 0 1^6 15 1 (0,0,0) 331 4,5,6,8,10 222 2,5,9,10,11 4 (1/2,1/2,1/2) 31111 9,11,12,13 42 1,4,6,7 (3/2,3/2,1/2) 1^7 15 6 0,3 1 (5/2,3/2,1/2)=rho 322 7 33 8 (1,1,0) 511 1,2,3 2211 12,13,14 not even Duality of cells: sp(6) SO(4,3) A_q for Sp(6) 0 15 3 1 11 1,11 2 10 0,15 3 14 4 4 9 7,10 5 8 2,13 6 12 5,9,12 7 13 6,8,14 8 7 16 9 6 17 10 5 18 11 4 12 3 27 13 2 29 14 1 15 0 50 All AV for Sp(6) are irreducible except possibly cells 11,13 11 is reducible: see orbit 331 cell 13 -> Sp(6)-orbit 2211 not even; can't say anything about it ------------------------------------------------------------------- special special dual orbit cells dual orbit cells #O_R lambda 7 0 1^6 15 1 (0,0,0) stable -S 1,2,3 -c 0 Irreducibles (living at lambda): 0 0( 0,44): 0 0 [i1,i1,i2] 1 2 0 ( 3, *) ( 4, *) ( 5, 6) Dual parameters: 50 stable: cells stable sums 0 0 (LDS) ------------------------------------------------------------------- special special dual orbit cells dual orbit cells #O_R lambda 331 4,5,6,8,10 222 2,5,9,10,11 4 (1/2,1/2,1/2) sophus-t43:SO43% stable -c 4,5,6,8,10 -S 1,2 Irreducibles (living at lambda): 16,34,35,45,47 16(11,34): 2 1 [C+,i2,C-] 27 16 4 ( *, *) (19,20) ( *, *) 3,2,3 34(19,17): 4 3 [C+,C+,C-] 41 44 17 ( *, *) ( *, *) ( *, *) 3,2,3,1,2,3 35(19,18): 4 3 [C+,C+,C-] 42 43 18 ( *, *) ( *, *) ( *, *) 3,2,3,1,2,3 45(24, 0): 6 5 [rn,rn,r2] 45 45 46 ( *, *) ( *, *) (40, *) 3,2,3,2,1,2,3,2,1 47(24, 2): 6 5 [rn,rn,r2] 47 47 52 ( *, *) ( *, *) (38, *) 3,2,3,2,1,2,3,2,1 Dual parameters: 36,17,18,0,2 Dimension of space of stable characters: 4 stable: cells stable sums 10 47 8 45 4,5 16+34 4,6 16+35 [5,6 -34+35 (extra)] Cell 4 for SO(4,3) is dual to cell 11 for Sp(6) with reducible AV: Associated cycles and varieties for Sp(6): AV(cell 2) = real form #1 of 222 AV(cell 5) = real form #2 of 222 AV(cell 9) = real form #3 of 222 AV(cell 10) = real form #4 of 222 AV(cell 11) = real form #3,#4 of 222 (reducible) ------------------------------------------------------------------- special special dual orbit cells dual orbit cells #O_R lambda 7 0 1^6 15 1 (0,0,0) 331 4,5,6,8,10 222 2,5,9,10,11 (1/2,1/2,1/2) 31111 9,11,12,13 42 1,4,6,7 (3/2,3/2,1/2) 1^7 15 6 0,3 1 (5/2,3/2,1/2)=rho 322 7 33 8 (1,1,0) special special dual orbit cells dual orbit cells #O_R lambda 7 0 1^6 15 1 (0,0,0) 331 4,5,6,8,10 222 2,5,9,10,11 (1/2,1/2,1/2) 31111 9,11,12,13 42 1,4,6,7 (3/2,3/2,1/2) 1^7 15 6 0,3 1 (5/2,3/2,1/2)=rho 322 7 33 8 (1,1,0) special special dual orbit cells dual orbit cells #O_R lambda 7 0 1^6 15 1 (0,0,0) 331 4,5,6,8,10 222 2,5,9,10,11 (1/2,1/2,1/2) 31111 9,11,12,13 42 1,4,6,7 (3/2,3/2,1/2) 1^7 15 6 0,3 1 (5/2,3/2,1/2)=rho 322 7 33 8 (1,1,0)