Spin(7,2) Double Cover
Infinitesimal characater: 1 integer(s) 3 half-integer(s)
Atlas K\G/B: kgb
Number of Blocks: 4
Block Size: 21
Blocks by Infinitesimal Character
Block 0
Infinitesimal Character (3.0, 2.5, 1.5, 0.5)
0( 0): * 0 0 0 ( 2, *) ( *, *) ( *, *) ( *, *) [i1,ic,ic,ic] 0
1( 2): * 1 1 1 ( 3, *) ( *, *) ( *, *) ( *, *) [i1,ic,ic,ic] 0
2( 8): * 5 2 2 ( 0, *) ( *, *) ( *, *) ( *, *) [r1,C+,ic,ic] 1
3( 9): * 4 3 3 ( 1, *) ( *, *) ( *, *) ( *, *) [r1,C+,ic,ic] 1
4(15): * 3 6 4 ( *, *) ( *, *) ( *, *) ( *, *) [Cn,C-,C+,ic] 2
5(16): * 2 7 5 ( *, *) ( *, *) ( *, *) ( *, *) [Cn,C-,C+,ic] 2
6(24): * 6 4 10 ( *, *) ( *, *) ( *, *) ( *, *) [Cn,ic,C-,C+] 3
7(25): * 7 5 9 ( *, *) ( *, *) ( *, *) ( *, *) [Cn,ic,C-,C+] 3
8(29): * 8 8 8 ( *, *) ( *, *) ( *, *) (11,12) [Cn,ic,ic,i2] 4
9(32): * 9 14 7 ( *, *) ( *, *) ( *, *) ( *, *) [Cn,ic,C+,C-] 4
10(33): * 10 13 6 ( *, *) ( *, *) ( *, *) ( *, *) [Cn,ic,C+,C-] 4
11(35): * 11 15 12 ( *, *) ( *, *) ( *, *) ( 8, *) [Cn,ic,C+,r2] 5
12(35): * 12 16 11 ( *, *) ( *, *) ( *, *) ( 8, *) [Cn,ic,C+,r2] 5
13(36): * 17 10 13 ( *, *) ( *, *) ( *, *) ( *, *) [Cn,C+,C-,ic] 5
14(37): * 18 9 14 ( *, *) ( *, *) ( *, *) ( *, *) [Cn,C+,C-,ic] 5
15(38): * 19 11 15 ( *, *) ( *, *) ( *, *) ( *, *) [Cn,C+,C-,ic] 6
16(38): * 20 12 16 ( *, *) ( *, *) ( *, *) ( *, *) [Cn,C+,C-,ic] 6
17(39): * 13 17 17 (19, *) ( *, *) ( *, *) ( *, *) [i1,C-,ic,ic] 6
18(40): * 14 18 18 (20, *) ( *, *) ( *, *) ( *, *) [i1,C-,ic,ic] 6
19(41): * 15 19 19 (17, *) ( *, *) ( *, *) ( *, *) [r1,C-,ic,ic] 7
20(41): * 16 20 20 (18, *) ( *, *) ( *, *) ( *, *) [r1,C-,ic,ic] 7
Kgb Graph
Block Text
Block Graph
R-Polynomial List
R-Polynomial Basis
KL-Polynomial List
KL-Polynomial Basis
Block 1
Infinitesimal Character (2.5, 2.0, 1.5, 0.5)
0( 1): * * 0 0 ( 2, *) ( 4, *) ( *, *) ( *, *) [i1,i1,ic,ic] 0
1( 4): * * 1 1 ( 3, *) ( 5, *) ( *, *) ( *, *) [i1,i1,ic,ic] 0
2( 8): * * 2 2 ( 0, *) ( *, *) ( *, *) ( *, *) [r1,Cn,ic,ic] 1
3( 9): * * 3 3 ( 1, *) ( *, *) ( *, *) ( *, *) [r1,Cn,ic,ic] 1
4(10): * * 7 4 ( *, *) ( 0, *) ( *, *) ( *, *) [Cn,r1,C+,ic] 1
5(11): * * 6 5 ( *, *) ( 1, *) ( *, *) ( *, *) [Cn,r1,C+,ic] 1
6(17): * * 5 9 ( *, *) ( *, *) ( *, *) ( *, *) [Cn,Cn,C-,C+] 2
7(18): * * 4 10 ( *, *) ( *, *) ( *, *) ( *, *) [Cn,Cn,C-,C+] 2
8(23): * * 8 8 ( *, *) ( *, *) ( *, *) (11,12) [Cn,Cn,ic,i2] 3
9(26): * * 14 6 ( *, *) ( *, *) ( *, *) ( *, *) [Cn,Cn,C+,C-] 3
10(27): * * 13 7 ( *, *) ( *, *) ( *, *) ( *, *) [Cn,Cn,C+,C-] 3
11(28): * * 15 12 ( *, *) ( *, *) ( *, *) ( 8, *) [Cn,Cn,C+,r2] 4
12(28): * * 16 11 ( *, *) ( *, *) ( *, *) ( 8, *) [Cn,Cn,C+,r2] 4
13(30): * * 10 13 ( *, *) (15, *) ( *, *) ( *, *) [Cn,i1,C-,ic] 4
14(31): * * 9 14 ( *, *) (16, *) ( *, *) ( *, *) [Cn,i1,C-,ic] 4
15(34): * * 11 15 ( *, *) (13, *) ( *, *) ( *, *) [Cn,r1,C-,ic] 5
16(34): * * 12 16 ( *, *) (14, *) ( *, *) ( *, *) [Cn,r1,C-,ic] 5
17(39): * * 17 17 (19, *) ( *, *) ( *, *) ( *, *) [i1,Cn,ic,ic] 6
18(40): * * 18 18 (20, *) ( *, *) ( *, *) ( *, *) [i1,Cn,ic,ic] 6
19(41): * * 19 19 (17, *) ( *, *) ( *, *) ( *, *) [r1,Cn,ic,ic] 7
20(41): * * 20 20 (18, *) ( *, *) ( *, *) ( *, *) [r1,Cn,ic,ic] 7
Kgb Graph
Block Text
Block Graph
R-Polynomial List
R-Polynomial Basis
KL-Polynomial List
KL-Polynomial Basis
Block 2
Infinitesimal Character (2.5, 1.5, 1.0, 0.5)
0( 3): 0 * * 0 ( *, *) ( 2, *) ( 4, *) ( *, *) [ic,i1,i1,ic] 0
1( 6): 1 * * 1 ( *, *) ( 3, *) ( 5, *) ( *, *) [ic,i1,i1,ic] 0
2(10): 7 * * 2 ( *, *) ( 0, *) ( *, *) ( *, *) [C+,r1,Cn,ic] 1
3(11): 6 * * 3 ( *, *) ( 1, *) ( *, *) ( *, *) [C+,r1,Cn,ic] 1
4(12): 4 * * 10 ( *, *) ( *, *) ( 0, *) ( *, *) [ic,Cn,r1,C+] 1
5(13): 5 * * 9 ( *, *) ( *, *) ( 1, *) ( *, *) [ic,Cn,r1,C+] 1
6(15): 3 * * 6 ( *, *) ( *, *) ( *, *) ( *, *) [C-,Cn,Cn,ic] 2
7(16): 2 * * 7 ( *, *) ( *, *) ( *, *) ( *, *) [C-,Cn,Cn,ic] 2
8(19): 8 * * 8 ( *, *) ( *, *) ( *, *) (11,12) [ic,Cn,Cn,i2] 2
9(20): 9 * * 5 ( *, *) ( *, *) (11, *) ( *, *) [ic,Cn,i1,C-] 2
10(21): 10 * * 4 ( *, *) ( *, *) (12, *) ( *, *) [ic,Cn,i1,C-] 2
11(22): 11 * * 12 ( *, *) ( *, *) ( 9, *) ( 8, *) [ic,Cn,r1,r2] 3
12(22): 12 * * 11 ( *, *) ( *, *) (10, *) ( 8, *) [ic,Cn,r1,r2] 3
13(30): 18 * * 13 ( *, *) (15, *) ( *, *) ( *, *) [C+,i1,Cn,ic] 4
14(31): 17 * * 14 ( *, *) (16, *) ( *, *) ( *, *) [C+,i1,Cn,ic] 4
15(34): 19 * * 15 ( *, *) (13, *) ( *, *) ( *, *) [C+,r1,Cn,ic] 5
16(34): 20 * * 16 ( *, *) (14, *) ( *, *) ( *, *) [C+,r1,Cn,ic] 5
17(36): 14 * * 17 ( *, *) ( *, *) ( *, *) ( *, *) [C-,Cn,Cn,ic] 5
18(37): 13 * * 18 ( *, *) ( *, *) ( *, *) ( *, *) [C-,Cn,Cn,ic] 5
19(38): 15 * * 19 ( *, *) ( *, *) ( *, *) ( *, *) [C-,Cn,Cn,ic] 6
20(38): 16 * * 20 ( *, *) ( *, *) ( *, *) ( *, *) [C-,Cn,Cn,ic] 6
Kgb Graph
Block Text
Block Graph
R-Polynomial List
R-Polynomial Basis
KL-Polynomial List
KL-Polynomial Basis
Block 3
Infinitesimal Character (3.5, 2.5, 1.5, 1.0)
0( 5): 0 0 * 1 ( *, *) ( *, *) ( 3, *) ( 4, *) [ic,ic,i1,i1] 0
1( 7): 1 1 * 0 ( *, *) ( *, *) ( 2, *) ( 4, *) [ic,ic,i1,i1] 0
2(12): 2 6 * 8 ( *, *) ( *, *) ( 1, *) ( *, *) [ic,C+,r1,C+] 1
3(13): 3 5 * 7 ( *, *) ( *, *) ( 0, *) ( *, *) [ic,C+,r1,C+] 1
4(14): 4 4 * 4 ( *, *) ( *, *) ( *, *) ( 1, 0) [ic,ic,Cn,r1] 1
5(17): 11 3 * 13 ( *, *) ( *, *) ( *, *) ( *, *) [C+,C-,Cn,C+] 2
6(18): 12 2 * 14 ( *, *) ( *, *) ( *, *) ( *, *) [C+,C-,Cn,C+] 2
7(20): 7 13 * 3 ( *, *) ( *, *) ( 9, *) ( *, *) [ic,C+,i1,C-] 2
8(21): 8 14 * 2 ( *, *) ( *, *) (10, *) ( *, *) [ic,C+,i1,C-] 2
9(22): 9 15 * 9 ( *, *) ( *, *) ( 7, *) ( *, *) [ic,C+,r1,rn] 3
10(22): 10 16 * 10 ( *, *) ( *, *) ( 8, *) ( *, *) [ic,C+,r1,rn] 3
11(24): 5 11 * 18 ( *, *) ( *, *) ( *, *) ( *, *) [C-,ic,Cn,C+] 3
12(25): 6 12 * 17 ( *, *) ( *, *) ( *, *) ( *, *) [C-,ic,Cn,C+] 3
13(26): 18 7 * 5 ( *, *) ( *, *) ( *, *) ( *, *) [C+,C-,Cn,C-] 3
14(27): 17 8 * 6 ( *, *) ( *, *) ( *, *) ( *, *) [C+,C-,Cn,C-] 3
15(28): 19 9 * 15 ( *, *) ( *, *) ( *, *) ( *, *) [C+,C-,Cn,rn] 4
16(28): 20 10 * 16 ( *, *) ( *, *) ( *, *) ( *, *) [C+,C-,Cn,rn] 4
17(32): 14 17 * 12 ( *, *) ( *, *) ( *, *) ( *, *) [C-,ic,Cn,C-] 4
18(33): 13 18 * 11 ( *, *) ( *, *) ( *, *) ( *, *) [C-,ic,Cn,C-] 4
19(35): 15 19 * 19 ( *, *) ( *, *) ( *, *) ( *, *) [C-,ic,Cn,rn] 5
20(35): 16 20 * 20 ( *, *) ( *, *) ( *, *) ( *, *) [C-,ic,Cn,rn] 5
Kgb Graph
Block Text
Block Graph
R-Polynomial List
R-Polynomial Basis
KL-Polynomial List
KL-Polynomial Basis