Spin(6,3) Double Cover
Infinitesimal characater: 3 integer(s) 1 half-integer(s)
Atlas K\G/B: kgb
Number of Blocks: 4
Block Size: 38
Blocks by Infinitesimal Character
Block 0
Infinitesimal Character (3.0, 2.0, 1.0, 0.5)
0( 2): 0 0 * 0 ( *, *) ( *, *) ( 2, *) ( *, *) [ic,ic,i1,ic] 0
1( 6): 1 1 * 1 ( *, *) ( *, *) ( 3, *) ( *, *) [ic,ic,i1,ic] 0
2(12): 2 4 * 7 ( *, *) ( *, *) ( 0, *) ( *, *) [ic,C+,r1,C+] 1
3(13): 3 5 * 8 ( *, *) ( *, *) ( 1, *) ( *, *) [ic,C+,r1,C+] 1
4(21): 13 2 * 15 ( *, *) ( *, *) ( *, *) ( *, *) [C+,C-,Cn,C+] 2
5(22): 14 3 * 16 ( *, *) ( *, *) ( *, *) ( *, *) [C+,C-,Cn,C+] 2
6(23): 6 12 * 6 ( *, *) ( *, *) ( *, *) (10,11) [ic,C+,Cn,i2] 2
7(26): 7 15 * 2 ( *, *) ( *, *) (11, *) ( *, *) [ic,C+,i1,C-] 2
8(27): 8 16 * 3 ( *, *) ( *, *) (10, *) ( *, *) [ic,C+,i1,C-] 2
9(28): 18 17 * 21 ( *, *) ( *, *) ( *, *) ( *, *) [C+,C+,Cn,C+] 3
10(31): 10 19 * 11 ( *, *) ( *, *) ( 8, *) ( 6, *) [ic,C+,r1,r2] 3
11(31): 11 20 * 10 ( *, *) ( *, *) ( 7, *) ( 6, *) [ic,C+,r1,r2] 3
12(32): 22 6 * 12 ( *, *) ( *, *) (17, *) (19,20) [C+,C-,i1,i2] 3
13(35): 4 13 * 23 ( *, *) ( *, *) ( *, *) ( *, *) [C-,ic,Cn,C+] 3
14(36): 5 14 * 24 ( *, *) ( *, *) ( *, *) ( *, *) [C-,ic,Cn,C+] 3
15(37): 23 7 * 4 ( *, *) ( *, *) ( *, *) ( *, *) [C+,C-,Cn,C-] 3
16(38): 24 8 * 5 ( *, *) ( *, *) ( *, *) ( *, *) [C+,C-,Cn,C-] 3
17(40): 25 9 * 30 ( *, *) ( *, *) (12, *) ( *, *) [C+,C-,r1,C+] 4
18(41): 9 26 * 29 ( *, *) ( *, *) ( *, *) ( *, *) [C-,C+,Cn,C+] 4
19(42): 27 10 * 20 ( *, *) ( *, *) ( *, *) (12, *) [C+,C-,Cn,r2] 4
20(42): 28 11 * 19 ( *, *) ( *, *) ( *, *) (12, *) [C+,C-,Cn,r2] 4
21(43): 29 30 * 9 ( *, *) ( *, *) ( *, *) ( *, *) [C+,C+,Cn,C-] 4
22(44): 12 22 * 22 ( *, *) ( *, *) (25, *) (27,28) [C-,ic,i1,i2] 4
23(49): 15 23 * 13 ( *, *) ( *, *) ( *, *) ( *, *) [C-,ic,Cn,C-] 4
24(50): 16 24 * 14 ( *, *) ( *, *) ( *, *) ( *, *) [C-,ic,Cn,C-] 4
25(52): 17 32 * 34 ( *, *) ( *, *) (22, *) ( *, *) [C-,C+,r1,C+] 5
26(53): 32 18 * 33 ( *, *) ( *, *) ( *, *) ( *, *) [C+,C-,Cn,C+] 5
27(55): 19 27 * 28 ( *, *) ( *, *) ( *, *) (22, *) [C-,ic,Cn,r2] 5
28(55): 20 28 * 27 ( *, *) ( *, *) ( *, *) (22, *) [C-,ic,Cn,r2] 5
29(56): 21 33 * 18 ( *, *) ( *, *) ( *, *) ( *, *) [C-,C+,Cn,C-] 5
30(57): 34 21 * 17 ( *, *) ( *, *) (31, *) ( *, *) [C+,C-,i2,C-] 5
31(61): 35 31 * 31 ( *, *) ( *, *) (30, *) ( *, *) [C+,rn,r1,rn] 6
32(62): 26 25 * 36 ( *, *) ( *, *) ( *, *) ( *, *) [C-,C-,Cn,C+] 6
33(64): 36 29 * 26 ( *, *) ( *, *) ( *, *) ( *, *) [C+,C-,Cn,C-] 6
34(65): 30 36 * 25 ( *, *) ( *, *) (35, *) ( *, *) [C-,C+,i2,C-] 6
35(69): 31 37 * 35 ( *, *) ( *, *) (34, *) ( *, *) [C-,C+,r1,rn] 7
36(73): 33 34 * 32 ( *, *) ( *, *) ( *, *) ( *, *) [C-,C-,Cn,C-] 7
37(74): 37 35 * 37 ( *, *) ( *, *) ( *, *) ( *, *) [rn,C-,Cn,rn] 8
Kgb Graph
Block Text
Block Graph
R-Polynomial List
R-Polynomial Basis
KL-Polynomial List
KL-Polynomial Basis
Block 1
Infinitesimal Character (3.0, 2.0, 1.5, 1.0)
0( 0): 0 * * 1 ( *, *) ( 2, *) ( 4, *) ( 6, *) [ic,i1,i1,i1] 0
1( 3): 1 * * 0 ( *, *) ( 3, *) ( 5, *) ( 6, *) [ic,i1,i1,i1] 0
2(10): 8 * * 3 ( *, *) ( 0, *) ( *, *) ( 7, *) [C+,r1,Cn,i1] 1
3(11): 9 * * 2 ( *, *) ( 1, *) ( *, *) ( 7, *) [C+,r1,Cn,i1] 1
4(12): 4 * * 10 ( *, *) ( *, *) ( 0, *) ( *, *) [ic,Cn,r1,C+] 1
5(13): 5 * * 11 ( *, *) ( *, *) ( 1, *) ( *, *) [ic,Cn,r1,C+] 1
6(16): 6 * * 6 ( *, *) ( 7, *) ( *, *) ( 1, 0) [ic,i1,Cn,r1] 1
7(18): 12 * * 7 ( *, *) ( 6, *) ( *, *) ( 3, 2) [C+,r1,Cn,r1] 2
8(19): 2 * * 9 ( *, *) ( *, *) ( *, *) (12, *) [C-,Cn,Cn,i1] 2
9(20): 3 * * 8 ( *, *) ( *, *) ( *, *) (12, *) [C-,Cn,Cn,i1] 2
10(26): 10 * * 4 ( *, *) ( *, *) (14, *) ( *, *) [ic,Cn,i1,C-] 2
11(27): 11 * * 5 ( *, *) ( *, *) (13, *) ( *, *) [ic,Cn,i1,C-] 2
12(30): 7 * * 12 ( *, *) ( *, *) ( *, *) ( 9, 8) [C-,Cn,Cn,r1] 3
13(31): 13 * * 13 ( *, *) ( *, *) (11, *) ( *, *) [ic,Cn,r1,rn] 3
14(31): 14 * * 14 ( *, *) ( *, *) (10, *) ( *, *) [ic,Cn,r1,rn] 3
15(33): 18 * * 15 ( *, *) ( *, *) (17, *) ( *, *) [C+,Cn,i1,ic] 3
16(39): 21 * * 16 ( *, *) ( *, *) ( *, *) ( *, *) [C+,Cn,Cn,ic] 4
17(40): 22 * * 25 ( *, *) ( *, *) (15, *) ( *, *) [C+,Cn,r1,C+] 4
18(45): 15 * * 18 ( *, *) (21, *) (22, *) ( *, *) [C-,i1,i1,ic] 4
19(47): 27 * * 20 ( *, *) (23, *) ( *, *) (26, *) [C+,i1,Cn,i1] 4
20(48): 28 * * 19 ( *, *) (24, *) ( *, *) (26, *) [C+,i1,Cn,i1] 4
21(51): 16 * * 21 ( *, *) (18, *) ( *, *) ( *, *) [C-,r1,Cn,ic] 5
22(52): 17 * * 32 ( *, *) ( *, *) (18, *) ( *, *) [C-,Cn,r1,C+] 5
23(54): 30 * * 24 ( *, *) (19, *) ( *, *) (29, *) [C+,r1,Cn,i2] 5
24(54): 31 * * 23 ( *, *) (20, *) ( *, *) (29, *) [C+,r1,Cn,i2] 5
25(57): 32 * * 17 ( *, *) ( *, *) (29, *) ( *, *) [C+,Cn,i2,C-] 5
26(58): 33 * * 26 ( *, *) (29, *) ( *, *) (20,19) [C+,i2,Cn,r1] 5
27(59): 19 * * 28 ( *, *) ( *, *) ( *, *) (33, *) [C-,Cn,Cn,i1] 5
28(60): 20 * * 27 ( *, *) ( *, *) ( *, *) (33, *) [C-,Cn,Cn,i1] 5
29(61): 34 * * 29 ( *, *) (26, *) (25, *) (23,24) [C+,r1,r1,r2] 6
30(63): 23 * * 31 ( *, *) ( *, *) ( *, *) (34, *) [C-,Cn,Cn,i2] 6
31(63): 24 * * 30 ( *, *) ( *, *) ( *, *) (34, *) [C-,Cn,Cn,i2] 6
32(65): 25 * * 22 ( *, *) ( *, *) (34, *) ( *, *) [C-,Cn,i2,C-] 6
33(66): 26 * * 33 ( *, *) ( *, *) ( *, *) (28,27) [C-,Cn,Cn,r1] 6
34(69): 29 * * 34 ( *, *) ( *, *) (32, *) (30,31) [C-,Cn,r1,r2] 7
35(71): 36 * * 35 ( *, *) ( *, *) ( *, *) ( *, *) [C+,Cn,Cn,ic] 7
36(75): 35 * * 36 ( *, *) (37, *) ( *, *) ( *, *) [C-,i2,Cn,ic] 8
37(77): 37 * * 37 ( *, *) (36, *) ( *, *) ( *, *) [rn,r1,Cn,ic] 9
Kgb Graph
Block Text
Block Graph
R-Polynomial List
R-Polynomial Basis
KL-Polynomial List
KL-Polynomial Basis
Block 2
Infinitesimal Character (3.0, 2.5, 2.0, 1.0)
0( 1): * * 0 1 ( 3, *) ( 4, *) ( *, *) ( 6, *) [i1,i1,ic,i1] 0
1( 5): * * 1 0 ( 2, *) ( 5, *) ( *, *) ( 6, *) [i1,i1,ic,i1] 0
2( 8): * * 2 3 ( 1, *) ( *, *) ( *, *) ( 7, *) [r1,Cn,ic,i1] 1
3( 9): * * 3 2 ( 0, *) ( *, *) ( *, *) ( 7, *) [r1,Cn,ic,i1] 1
4(10): * * 9 5 ( *, *) ( 0, *) ( *, *) ( 8, *) [Cn,r1,C+,i1] 1
5(11): * * 10 4 ( *, *) ( 1, *) ( *, *) ( 8, *) [Cn,r1,C+,i1] 1
6(15): * * 11 6 ( 7, *) ( 8, *) ( *, *) ( 1, 0) [i1,i1,C+,r1] 1
7(17): * * 13 7 ( 6, *) ( *, *) ( *, *) ( 3, 2) [r1,Cn,C+,r1] 2
8(18): * * 12 8 ( *, *) ( 6, *) ( *, *) ( 5, 4) [Cn,r1,C+,r1] 2
9(21): * * 4 14 ( *, *) ( *, *) ( *, *) ( *, *) [Cn,Cn,C-,C+] 2
10(22): * * 5 15 ( *, *) ( *, *) ( *, *) ( *, *) [Cn,Cn,C-,C+] 2
11(24): * * 6 11 (13, *) ( *, *) ( *, *) ( *, *) [i1,Cn,C-,ic] 2
12(28): * * 8 18 ( *, *) ( *, *) ( *, *) ( *, *) [Cn,Cn,C-,C+] 3
13(29): * * 7 13 (11, *) ( *, *) ( *, *) ( *, *) [r1,Cn,C-,ic] 3
14(37): * * 20 9 ( *, *) ( *, *) ( *, *) ( *, *) [Cn,Cn,C+,C-] 3
15(38): * * 21 10 ( *, *) ( *, *) ( *, *) ( *, *) [Cn,Cn,C+,C-] 3
16(42): * * 23 16 ( *, *) ( *, *) ( *, *) ( *, *) [Cn,Cn,C+,rn] 4
17(42): * * 24 17 ( *, *) ( *, *) ( *, *) ( *, *) [Cn,Cn,C+,rn] 4
18(43): * * 25 12 ( *, *) ( *, *) ( *, *) ( *, *) [Cn,Cn,C+,C-] 4
19(46): * * 19 19 ( *, *) (22, *) ( *, *) ( *, *) [Cn,i1,ic,ic] 4
20(47): * * 14 21 ( *, *) (23, *) ( *, *) (25, *) [Cn,i1,C-,i1] 4
21(48): * * 15 20 ( *, *) (24, *) ( *, *) (25, *) [Cn,i1,C-,i1] 4
22(51): * * 27 22 ( *, *) (19, *) ( *, *) ( *, *) [Cn,r1,C+,ic] 5
23(54): * * 16 24 ( *, *) (20, *) ( *, *) (26, *) [Cn,r1,C-,i2] 5
24(54): * * 17 23 ( *, *) (21, *) ( *, *) (26, *) [Cn,r1,C-,i2] 5
25(58): * * 18 25 ( *, *) (26, *) ( *, *) (21,20) [Cn,i2,C-,r1] 5
26(61): * * 26 26 ( *, *) (25, *) ( *, *) (23,24) [Cn,r1,rn,r2] 6
27(62): * * 22 33 ( *, *) ( *, *) ( *, *) ( *, *) [Cn,Cn,C-,C+] 6
28(67): * * 28 29 (31, *) ( *, *) ( *, *) (32, *) [i1,Cn,ic,i1] 6
29(68): * * 29 28 (30, *) ( *, *) ( *, *) (32, *) [i1,Cn,ic,i1] 6
30(70): * * 30 31 (29, *) ( *, *) ( *, *) (34, *) [r1,Cn,ic,i2] 7
31(70): * * 31 30 (28, *) ( *, *) ( *, *) (34, *) [r1,Cn,ic,i2] 7
32(72): * * 36 32 (34, *) ( *, *) ( *, *) (29,28) [i2,Cn,C+,r1] 7
33(73): * * 35 27 ( *, *) ( *, *) ( *, *) ( *, *) [Cn,Cn,C+,C-] 7
34(74): * * 37 34 (32, *) ( *, *) ( *, *) (30,31) [r1,Cn,C+,r2] 8
35(75): * * 33 35 ( *, *) (37, *) ( *, *) ( *, *) [Cn,i2,C-,ic] 8
36(76): * * 32 36 (37, *) ( *, *) ( *, *) ( *, *) [i2,Cn,C-,ic] 8
37(77): * * 34 37 (36, *) (35, *) ( *, *) ( *, *) [r1,r1,C-,ic] 9
Kgb Graph
Block Text
Block Graph
R-Polynomial List
R-Polynomial Basis
KL-Polynomial List
KL-Polynomial Basis
Block 3
Infinitesimal Character (3.5, 3.0, 2.0, 1.0)
0( 4): * 0 0 1 ( 3, *) ( *, *) ( *, *) ( 4, *) [i1,ic,ic,i1] 0
1( 7): * 1 1 0 ( 2, *) ( *, *) ( *, *) ( 4, *) [i1,ic,ic,i1] 0
2( 8): * 7 2 3 ( 1, *) ( *, *) ( *, *) ( 5, *) [r1,C+,ic,i1] 1
3( 9): * 6 3 2 ( 0, *) ( *, *) ( *, *) ( 5, *) [r1,C+,ic,i1] 1
4(14): * 4 8 4 ( 5, *) ( *, *) ( *, *) ( 1, 0) [i1,ic,C+,r1] 1
5(17): * 10 9 5 ( 4, *) ( *, *) ( *, *) ( 3, 2) [r1,C+,C+,r1] 2
6(19): * 3 12 7 ( *, *) ( *, *) ( *, *) (10, *) [Cn,C-,C+,i1] 2
7(20): * 2 13 6 ( *, *) ( *, *) ( *, *) (10, *) [Cn,C-,C+,i1] 2
8(25): * 11 4 8 ( 9, *) ( *, *) ( *, *) ( *, *) [i1,C+,C-,ic] 2
9(29): * 14 5 9 ( 8, *) ( *, *) ( *, *) ( *, *) [r1,C+,C-,ic] 3
10(30): * 5 15 10 ( *, *) ( *, *) ( *, *) ( 7, 6) [Cn,C-,C+,r1] 3
11(34): * 8 11 11 ( *, *) ( *, *) ( *, *) ( *, *) [Cn,C-,ic,ic] 3
12(35): * 12 6 16 ( *, *) ( *, *) ( *, *) ( *, *) [Cn,ic,C-,C+] 3
13(36): * 13 7 17 ( *, *) ( *, *) ( *, *) ( *, *) [Cn,ic,C-,C+] 3
14(39): * 9 18 14 ( *, *) ( *, *) ( *, *) ( *, *) [Cn,C-,C+,ic] 4
15(41): * 18 10 21 ( *, *) ( *, *) ( *, *) ( *, *) [Cn,C+,C-,C+] 4
16(49): * 16 22 12 ( *, *) ( *, *) ( *, *) ( *, *) [Cn,ic,C+,C-] 4
17(50): * 17 23 13 ( *, *) ( *, *) ( *, *) ( *, *) [Cn,ic,C+,C-] 4
18(53): * 15 14 26 ( *, *) ( *, *) ( *, *) ( *, *) [Cn,C-,C-,C+] 5
19(55): * 19 24 19 ( *, *) ( *, *) ( *, *) ( *, *) [Cn,ic,C+,rn] 5
20(55): * 20 25 20 ( *, *) ( *, *) ( *, *) ( *, *) [Cn,ic,C+,rn] 5
21(56): * 26 27 15 ( *, *) ( *, *) ( *, *) ( *, *) [Cn,C+,C+,C-] 5
22(59): * 28 16 23 ( *, *) ( *, *) ( *, *) (27, *) [Cn,C+,C-,i1] 5
23(60): * 29 17 22 ( *, *) ( *, *) ( *, *) (27, *) [Cn,C+,C-,i1] 5
24(63): * 31 19 25 ( *, *) ( *, *) ( *, *) (30, *) [Cn,C+,C-,i2] 6
25(63): * 32 20 24 ( *, *) ( *, *) ( *, *) (30, *) [Cn,C+,C-,i2] 6
26(64): * 21 33 18 ( *, *) ( *, *) ( *, *) ( *, *) [Cn,C-,C+,C-] 6
27(66): * 34 21 27 ( *, *) ( *, *) ( *, *) (23,22) [Cn,C+,C-,r1] 6
28(67): * 22 28 29 (32, *) ( *, *) ( *, *) (34, *) [i1,C-,ic,i1] 6
29(68): * 23 29 28 (31, *) ( *, *) ( *, *) (34, *) [i1,C-,ic,i1] 6
30(69): * 35 30 30 ( *, *) ( *, *) ( *, *) (24,25) [Cn,C+,rn,r2] 7
31(70): * 24 31 32 (29, *) ( *, *) ( *, *) (35, *) [r1,C-,ic,i2] 7
32(70): * 25 32 31 (28, *) ( *, *) ( *, *) (35, *) [r1,C-,ic,i2] 7
33(71): * 36 26 33 ( *, *) ( *, *) ( *, *) ( *, *) [Cn,C+,C-,ic] 7
34(72): * 27 36 34 (35, *) ( *, *) ( *, *) (29,28) [i2,C-,C+,r1] 7
35(74): * 30 37 35 (34, *) ( *, *) ( *, *) (31,32) [r1,C-,C+,r2] 8
36(76): * 33 34 36 (37, *) ( *, *) ( *, *) ( *, *) [i2,C-,C-,ic] 8
37(77): * 37 35 37 (36, *) ( *, *) ( *, *) ( *, *) [r1,rn,C-,ic] 9
Kgb Graph
Block Text
Block Graph
R-Polynomial List
R-Polynomial Basis
KL-Polynomial List
KL-Polynomial Basis