Weight Multiplicities

Groups of type B6, degree bound 4000

Diagram:

1 < 2 - .. - 6

Overview

Dimension	Highest weight	Characteristic
1	[ 0, 0, 0, 0, 0, 0 ]	all
12	[ 0, 0, 0, 0, 0, 1 ]	2
13	[ 0, 0, 0, 0, 0, 1 ]	not 2
64	[ 0, 0, 0, 0, 1, 0 ]	2
64	[ 1, 0, 0, 0, 0, 0 ]	all
78	[ 0, 0, 0, 0, 1, 0 ]	not 2
89	[ 0, 0, 0, 0, 0, 2 ]	13
90	[ 0, 0, 0, 0, 0, 2 ]	not 2, 13
208	[ 0, 0, 0, 1, 0, 0 ]	2
286	[ 0, 0, 0, 1, 0, 0 ]	not 2
364	[ 0, 0, 1, 0, 0, 0 ]	2
416	[ 0, 0, 0, 0, 1, 1 ]	3
429	[ 0, 0, 0, 0, 0, 3 ]	5
442	[ 0, 0, 0, 0, 0, 3 ]	not 2, 3, 5
560	[ 0, 0, 0, 0, 1, 1 ]	2
560	[ 0, 1, 0, 0, 0, 0 ]	2
704	[ 1, 0, 0, 0, 0, 1 ]	13
715	[ 0, 0, 0, 0, 1, 1 ]	not 2, 3
715	[ 0, 0, 1, 0, 0, 0 ]	not 2
768	[ 1, 0, 0, 0, 0, 1 ]	not 13
1287	[ 0, 1, 0, 0, 0, 0 ]	not 2
1508	[ 0, 0, 0, 1, 0, 1 ]	2
1559	[ 0, 0, 0, 0, 2, 0 ]	3
1639	[ 0, 0, 0, 0, 0, 4 ]	17
1716	[ 2, 0, 0, 0, 0, 0 ]	not 2
1728	[ 0, 0, 0, 0, 0, 4 ]	5
1729	[ 0, 0, 0, 0, 0, 4 ]	not 2, 3, 5, 17
2185	[ 0, 0, 0, 0, 2, 0 ]	11
2275	[ 0, 0, 0, 0, 2, 0 ]	not 2, 3, 11
2847	[ 0, 0, 0, 1, 0, 1 ]	11
2925	[ 0, 0, 0, 1, 0, 1 ]	not 2, 11
3392	[ 1, 0, 0, 0, 1, 0 ]	11
3808	[ 0, 0, 1, 0, 0, 1 ]	2
3838	[ 0, 0, 0, 0, 1, 2 ]	13
3849	[ 0, 0, 0, 0, 1, 2 ]	3
3849	[ 0, 0, 0, 0, 1, 2 ]	5
3927	[ 0, 0, 0, 0, 1, 2 ]	not 2, 3, 5, 13

The characters

Highest weight: [ 0, 0, 0, 0, 0, 0 ]
Characteristic: all
Dimension: 1

Level	dominant weight	weight multiplicity	length of W-orbit
1	[ 0, 0, 0, 0, 0, 0 ]	1	1

Highest weight: [ 0, 0, 0, 0, 0, 1 ]
Characteristic: 2
Dimension: 12

Level	dominant weight	weight multiplicity	length of W-orbit
13	[ 0, 0, 0, 0, 0, 1 ]	1	12

Highest weight: [ 0, 0, 0, 0, 0, 1 ]
Characteristic: not 2
Dimension: 13

Level	dominant weight	weight multiplicity	length of W-orbit
13	[ 0, 0, 0, 0, 0, 1 ]	1	12
1	[ 0, 0, 0, 0, 0, 0 ]	1	1

Highest weight: [ 0, 0, 0, 0, 1, 0 ]
Characteristic: 2
Dimension: 64

Level	dominant weight	weight multiplicity	length of W-orbit
23	[ 0, 0, 0, 0, 1, 0 ]	1	60
1	[ 0, 0, 0, 0, 0, 0 ]	4	1

Highest weight: [ 1, 0, 0, 0, 0, 0 ]
Characteristic: all
Dimension: 64

Level	dominant weight	weight multiplicity	length of W-orbit
22	[ 1, 0, 0, 0, 0, 0 ]	1	64

Highest weight: [ 0, 0, 0, 0, 1, 0 ]
Characteristic: not 2
Dimension: 78

Level	dominant weight	weight multiplicity	length of W-orbit
23	[ 0, 0, 0, 0, 1, 0 ]	1	60
13	[ 0, 0, 0, 0, 0, 1 ]	1	12
1	[ 0, 0, 0, 0, 0, 0 ]	6	1

Highest weight: [ 0, 0, 0, 0, 0, 2 ]
Characteristic: 13
Dimension: 89

Level	dominant weight	weight multiplicity	length of W-orbit
25	[ 0, 0, 0, 0, 0, 2 ]	1	12
23	[ 0, 0, 0, 0, 1, 0 ]	1	60
13	[ 0, 0, 0, 0, 0, 1 ]	1	12
1	[ 0, 0, 0, 0, 0, 0 ]	5	1

Highest weight: [ 0, 0, 0, 0, 0, 2 ]
Characteristic: not 2,13
Dimension: 90

Level	dominant weight	weight multiplicity	length of W-orbit
25	[ 0, 0, 0, 0, 0, 2 ]	1	12
23	[ 0, 0, 0, 0, 1, 0 ]	1	60
13	[ 0, 0, 0, 0, 0, 1 ]	1	12
1	[ 0, 0, 0, 0, 0, 0 ]	6	1

Highest weight: [ 0, 0, 0, 1, 0, 0 ]
Characteristic: 2
Dimension: 208

Level	dominant weight	weight multiplicity	length of W-orbit
31	[ 0, 0, 0, 1, 0, 0 ]	1	160
13	[ 0, 0, 0, 0, 0, 1 ]	4	12

Highest weight: [ 0, 0, 0, 1, 0, 0 ]
Characteristic: not 2
Dimension: 286

Level	dominant weight	weight multiplicity	length of W-orbit
31	[ 0, 0, 0, 1, 0, 0 ]	1	160
23	[ 0, 0, 0, 0, 1, 0 ]	1	60
13	[ 0, 0, 0, 0, 0, 1 ]	5	12
1	[ 0, 0, 0, 0, 0, 0 ]	6	1

Highest weight: [ 0, 0, 1, 0, 0, 0 ]
Characteristic: 2
Dimension: 364

Level	dominant weight	weight multiplicity	length of W-orbit
37	[ 0, 0, 1, 0, 0, 0 ]	1	240
23	[ 0, 0, 0, 0, 1, 0 ]	2	60
1	[ 0, 0, 0, 0, 0, 0 ]	4	1

Highest weight: [ 0, 0, 0, 0, 1, 1 ]
Characteristic: 3
Dimension: 416

Level	dominant weight	weight multiplicity	length of W-orbit
35	[ 0, 0, 0, 0, 1, 1 ]	1	120
31	[ 0, 0, 0, 1, 0, 0 ]	1	160
25	[ 0, 0, 0, 0, 0, 2 ]	1	12
23	[ 0, 0, 0, 0, 1, 0 ]	1	60
13	[ 0, 0, 0, 0, 0, 1 ]	5	12
1	[ 0, 0, 0, 0, 0, 0 ]	4	1

Highest weight: [ 0, 0, 0, 0, 0, 3 ]
Characteristic: 5
Dimension: 429

Level	dominant weight	weight multiplicity	length of W-orbit
37	[ 0, 0, 0, 0, 0, 3 ]	1	12
35	[ 0, 0, 0, 0, 1, 1 ]	1	120
31	[ 0, 0, 0, 1, 0, 0 ]	1	160
25	[ 0, 0, 0, 0, 0, 2 ]	1	12
23	[ 0, 0, 0, 0, 1, 0 ]	1	60
13	[ 0, 0, 0, 0, 0, 1 ]	5	12
1	[ 0, 0, 0, 0, 0, 0 ]	5	1

Highest weight: [ 0, 0, 0, 0, 0, 3 ]
Characteristic: not 2,3,5
Dimension: 442

Level	dominant weight	weight multiplicity	length of W-orbit
37	[ 0, 0, 0, 0, 0, 3 ]	1	12
35	[ 0, 0, 0, 0, 1, 1 ]	1	120
31	[ 0, 0, 0, 1, 0, 0 ]	1	160
25	[ 0, 0, 0, 0, 0, 2 ]	1	12
23	[ 0, 0, 0, 0, 1, 0 ]	1	60
13	[ 0, 0, 0, 0, 0, 1 ]	6	12
1	[ 0, 0, 0, 0, 0, 0 ]	6	1

Highest weight: [ 0, 0, 0, 0, 1, 1 ]
Characteristic: 2
Dimension: 560

Level	dominant weight	weight multiplicity	length of W-orbit
35	[ 0, 0, 0, 0, 1, 1 ]	1	120
31	[ 0, 0, 0, 1, 0, 0 ]	2	160
13	[ 0, 0, 0, 0, 0, 1 ]	10	12

Highest weight: [ 0, 1, 0, 0, 0, 0 ]
Characteristic: 2
Dimension: 560

Level	dominant weight	weight multiplicity	length of W-orbit
41	[ 0, 1, 0, 0, 0, 0 ]	1	192
31	[ 0, 0, 0, 1, 0, 0 ]	2	160
13	[ 0, 0, 0, 0, 0, 1 ]	4	12

Highest weight: [ 1, 0, 0, 0, 0, 1 ]
Characteristic: 13
Dimension: 704

Level	dominant weight	weight multiplicity	length of W-orbit
34	[ 1, 0, 0, 0, 0, 1 ]	1	384
22	[ 1, 0, 0, 0, 0, 0 ]	5	64

Highest weight: [ 0, 0, 0, 0, 1, 1 ]
Characteristic: not 2,3
Dimension: 715

Level	dominant weight	weight multiplicity	length of W-orbit
35	[ 0, 0, 0, 0, 1, 1 ]	1	120
31	[ 0, 0, 0, 1, 0, 0 ]	2	160
25	[ 0, 0, 0, 0, 0, 2 ]	1	12
23	[ 0, 0, 0, 0, 1, 0 ]	2	60
13	[ 0, 0, 0, 0, 0, 1 ]	11	12
1	[ 0, 0, 0, 0, 0, 0 ]	11	1

Highest weight: [ 0, 0, 1, 0, 0, 0 ]
Characteristic: not 2
Dimension: 715

Level	dominant weight	weight multiplicity	length of W-orbit
37	[ 0, 0, 1, 0, 0, 0 ]	1	240
31	[ 0, 0, 0, 1, 0, 0 ]	1	160
23	[ 0, 0, 0, 0, 1, 0 ]	4	60
13	[ 0, 0, 0, 0, 0, 1 ]	5	12
1	[ 0, 0, 0, 0, 0, 0 ]	15	1

Highest weight: [ 1, 0, 0, 0, 0, 1 ]
Characteristic: not 13
Dimension: 768

Level	dominant weight	weight multiplicity	length of W-orbit
34	[ 1, 0, 0, 0, 0, 1 ]	1	384
22	[ 1, 0, 0, 0, 0, 0 ]	6	64

Highest weight: [ 0, 1, 0, 0, 0, 0 ]
Characteristic: not 2
Dimension: 1287

Level	dominant weight	weight multiplicity	length of W-orbit
41	[ 0, 1, 0, 0, 0, 0 ]	1	192
37	[ 0, 0, 1, 0, 0, 0 ]	1	240
31	[ 0, 0, 0, 1, 0, 0 ]	3	160
23	[ 0, 0, 0, 0, 1, 0 ]	4	60
13	[ 0, 0, 0, 0, 0, 1 ]	10	12
1	[ 0, 0, 0, 0, 0, 0 ]	15	1

Highest weight: [ 0, 0, 0, 1, 0, 1 ]
Characteristic: 2
Dimension: 1508

Level	dominant weight	weight multiplicity	length of W-orbit
43	[ 0, 0, 0, 1, 0, 1 ]	1	480
37	[ 0, 0, 1, 0, 0, 0 ]	2	240
25	[ 0, 0, 0, 0, 0, 2 ]	4	12
23	[ 0, 0, 0, 0, 1, 0 ]	8	60
1	[ 0, 0, 0, 0, 0, 0 ]	20	1

Highest weight: [ 0, 0, 0, 0, 2, 0 ]
Characteristic: 3
Dimension: 1559

Level	dominant weight	weight multiplicity	length of W-orbit
45	[ 0, 0, 0, 0, 2, 0 ]	1	60
43	[ 0, 0, 0, 1, 0, 1 ]	1	480
37	[ 0, 0, 1, 0, 0, 0 ]	1	240
35	[ 0, 0, 0, 0, 1, 1 ]	1	120
31	[ 0, 0, 0, 1, 0, 0 ]	1	160
25	[ 0, 0, 0, 0, 0, 2 ]	5	12
23	[ 0, 0, 0, 0, 1, 0 ]	6	60
13	[ 0, 0, 0, 0, 0, 1 ]	5	12
1	[ 0, 0, 0, 0, 0, 0 ]	19	1

Highest weight: [ 0, 0, 0, 0, 0, 4 ]
Characteristic: 17
Dimension: 1639

Level	dominant weight	weight multiplicity	length of W-orbit
49	[ 0, 0, 0, 0, 0, 4 ]	1	12
47	[ 0, 0, 0, 0, 1, 2 ]	1	120
45	[ 0, 0, 0, 0, 2, 0 ]	1	60
43	[ 0, 0, 0, 1, 0, 1 ]	1	480
37	[ 0, 0, 1, 0, 0, 0 ]	1	240
37	[ 0, 0, 0, 0, 0, 3 ]	1	12
35	[ 0, 0, 0, 0, 1, 1 ]	1	120
31	[ 0, 0, 0, 1, 0, 0 ]	1	160
25	[ 0, 0, 0, 0, 0, 2 ]	5	12
23	[ 0, 0, 0, 0, 1, 0 ]	5	60
13	[ 0, 0, 0, 0, 0, 1 ]	5	12
1	[ 0, 0, 0, 0, 0, 0 ]	15	1

Highest weight: [ 2, 0, 0, 0, 0, 0 ]
Characteristic: not 2
Dimension: 1716

Level	dominant weight	weight multiplicity	length of W-orbit
43	[ 2, 0, 0, 0, 0, 0 ]	1	64
41	[ 0, 1, 0, 0, 0, 0 ]	1	192
37	[ 0, 0, 1, 0, 0, 0 ]	2	240
31	[ 0, 0, 0, 1, 0, 0 ]	3	160
23	[ 0, 0, 0, 0, 1, 0 ]	6	60
13	[ 0, 0, 0, 0, 0, 1 ]	10	12
1	[ 0, 0, 0, 0, 0, 0 ]	20	1

Highest weight: [ 0, 0, 0, 0, 0, 4 ]
Characteristic: 5
Dimension: 1728

Level	dominant weight	weight multiplicity	length of W-orbit
49	[ 0, 0, 0, 0, 0, 4 ]	1	12
47	[ 0, 0, 0, 0, 1, 2 ]	1	120
45	[ 0, 0, 0, 0, 2, 0 ]	1	60
43	[ 0, 0, 0, 1, 0, 1 ]	1	480
37	[ 0, 0, 1, 0, 0, 0 ]	1	240
37	[ 0, 0, 0, 0, 0, 3 ]	1	12
35	[ 0, 0, 0, 0, 1, 1 ]	1	120
31	[ 0, 0, 0, 1, 0, 0 ]	1	160
25	[ 0, 0, 0, 0, 0, 2 ]	6	12
23	[ 0, 0, 0, 0, 1, 0 ]	6	60
13	[ 0, 0, 0, 0, 0, 1 ]	6	12
1	[ 0, 0, 0, 0, 0, 0 ]	20	1

Highest weight: [ 0, 0, 0, 0, 0, 4 ]
Characteristic: not 2,3,5,17
Dimension: 1729

Level	dominant weight	weight multiplicity	length of W-orbit
49	[ 0, 0, 0, 0, 0, 4 ]	1	12
47	[ 0, 0, 0, 0, 1, 2 ]	1	120
45	[ 0, 0, 0, 0, 2, 0 ]	1	60
43	[ 0, 0, 0, 1, 0, 1 ]	1	480
37	[ 0, 0, 1, 0, 0, 0 ]	1	240
37	[ 0, 0, 0, 0, 0, 3 ]	1	12
35	[ 0, 0, 0, 0, 1, 1 ]	1	120
31	[ 0, 0, 0, 1, 0, 0 ]	1	160
25	[ 0, 0, 0, 0, 0, 2 ]	6	12
23	[ 0, 0, 0, 0, 1, 0 ]	6	60
13	[ 0, 0, 0, 0, 0, 1 ]	6	12
1	[ 0, 0, 0, 0, 0, 0 ]	21	1

Highest weight: [ 0, 0, 0, 0, 2, 0 ]
Characteristic: 11
Dimension: 2185

Level	dominant weight	weight multiplicity	length of W-orbit
45	[ 0, 0, 0, 0, 2, 0 ]	1	60
43	[ 0, 0, 0, 1, 0, 1 ]	1	480
37	[ 0, 0, 1, 0, 0, 0 ]	2	240
35	[ 0, 0, 0, 0, 1, 1 ]	1	120
31	[ 0, 0, 0, 1, 0, 0 ]	2	160
25	[ 0, 0, 0, 0, 0, 2 ]	4	12
23	[ 0, 0, 0, 0, 1, 0 ]	9	60
13	[ 0, 0, 0, 0, 0, 1 ]	9	12
1	[ 0, 0, 0, 0, 0, 0 ]	29	1

Highest weight: [ 0, 0, 0, 0, 2, 0 ]
Characteristic: not 2,3,11
Dimension: 2275

Level	dominant weight	weight multiplicity	length of W-orbit
45	[ 0, 0, 0, 0, 2, 0 ]	1	60
43	[ 0, 0, 0, 1, 0, 1 ]	1	480
37	[ 0, 0, 1, 0, 0, 0 ]	2	240
35	[ 0, 0, 0, 0, 1, 1 ]	1	120
31	[ 0, 0, 0, 1, 0, 0 ]	2	160
25	[ 0, 0, 0, 0, 0, 2 ]	5	12
23	[ 0, 0, 0, 0, 1, 0 ]	10	60
13	[ 0, 0, 0, 0, 0, 1 ]	10	12
1	[ 0, 0, 0, 0, 0, 0 ]	35	1

Highest weight: [ 0, 0, 0, 1, 0, 1 ]
Characteristic: 11
Dimension: 2847

Level	dominant weight	weight multiplicity	length of W-orbit
43	[ 0, 0, 0, 1, 0, 1 ]	1	480
37	[ 0, 0, 1, 0, 0, 0 ]	3	240
35	[ 0, 0, 0, 0, 1, 1 ]	1	120
31	[ 0, 0, 0, 1, 0, 0 ]	3	160
25	[ 0, 0, 0, 0, 0, 2 ]	5	12
23	[ 0, 0, 0, 0, 1, 0 ]	13	60
13	[ 0, 0, 0, 0, 0, 1 ]	14	12
1	[ 0, 0, 0, 0, 0, 0 ]	39	1

Highest weight: [ 0, 0, 0, 1, 0, 1 ]
Characteristic: not 2,11
Dimension: 2925

Level	dominant weight	weight multiplicity	length of W-orbit
43	[ 0, 0, 0, 1, 0, 1 ]	1	480
37	[ 0, 0, 1, 0, 0, 0 ]	3	240
35	[ 0, 0, 0, 0, 1, 1 ]	1	120
31	[ 0, 0, 0, 1, 0, 0 ]	3	160
25	[ 0, 0, 0, 0, 0, 2 ]	5	12
23	[ 0, 0, 0, 0, 1, 0 ]	14	60
13	[ 0, 0, 0, 0, 0, 1 ]	15	12
1	[ 0, 0, 0, 0, 0, 0 ]	45	1

Highest weight: [ 1, 0, 0, 0, 1, 0 ]
Characteristic: 11
Dimension: 3392

Level	dominant weight	weight multiplicity	length of W-orbit
44	[ 1, 0, 0, 0, 1, 0 ]	1	960
34	[ 1, 0, 0, 0, 0, 1 ]	4	384
22	[ 1, 0, 0, 0, 0, 0 ]	14	64

Highest weight: [ 0, 0, 1, 0, 0, 1 ]
Characteristic: 2
Dimension: 3808

Level	dominant weight	weight multiplicity	length of W-orbit
49	[ 0, 0, 1, 0, 0, 1 ]	1	960
41	[ 0, 1, 0, 0, 0, 0 ]	4	192
35	[ 0, 0, 0, 0, 1, 1 ]	2	120
31	[ 0, 0, 0, 1, 0, 0 ]	10	160
13	[ 0, 0, 0, 0, 0, 1 ]	20	12

Highest weight: [ 0, 0, 0, 0, 1, 2 ]
Characteristic: 13
Dimension: 3838

Level	dominant weight	weight multiplicity	length of W-orbit
47	[ 0, 0, 0, 0, 1, 2 ]	1	120
45	[ 0, 0, 0, 0, 2, 0 ]	1	60
43	[ 0, 0, 0, 1, 0, 1 ]	2	480
37	[ 0, 0, 1, 0, 0, 0 ]	3	240
37	[ 0, 0, 0, 0, 0, 3 ]	1	12
35	[ 0, 0, 0, 0, 1, 1 ]	2	120
31	[ 0, 0, 0, 1, 0, 0 ]	3	160
25	[ 0, 0, 0, 0, 0, 2 ]	10	12
23	[ 0, 0, 0, 0, 1, 0 ]	15	60
13	[ 0, 0, 0, 0, 0, 1 ]	15	12
1	[ 0, 0, 0, 0, 0, 0 ]	46	1

Highest weight: [ 0, 0, 0, 0, 1, 2 ]
Characteristic: 3
Dimension: 3849

Level	dominant weight	weight multiplicity	length of W-orbit
47	[ 0, 0, 0, 0, 1, 2 ]	1	120
45	[ 0, 0, 0, 0, 2, 0 ]	1	60
43	[ 0, 0, 0, 1, 0, 1 ]	2	480
37	[ 0, 0, 1, 0, 0, 0 ]	3	240
37	[ 0, 0, 0, 0, 0, 3 ]	1	12
35	[ 0, 0, 0, 0, 1, 1 ]	2	120
31	[ 0, 0, 0, 1, 0, 0 ]	3	160
25	[ 0, 0, 0, 0, 0, 2 ]	11	12
23	[ 0, 0, 0, 0, 1, 0 ]	15	60
13	[ 0, 0, 0, 0, 0, 1 ]	15	12
1	[ 0, 0, 0, 0, 0, 0 ]	45	1

Highest weight: [ 0, 0, 0, 0, 1, 2 ]
Characteristic: 5
Dimension: 3849

Level	dominant weight	weight multiplicity	length of W-orbit
47	[ 0, 0, 0, 0, 1, 2 ]	1	120
45	[ 0, 0, 0, 0, 2, 0 ]	1	60
43	[ 0, 0, 0, 1, 0, 1 ]	2	480
37	[ 0, 0, 1, 0, 0, 0 ]	3	240
37	[ 0, 0, 0, 0, 0, 3 ]	1	12
35	[ 0, 0, 0, 0, 1, 1 ]	2	120
31	[ 0, 0, 0, 1, 0, 0 ]	3	160
25	[ 0, 0, 0, 0, 0, 2 ]	11	12
23	[ 0, 0, 0, 0, 1, 0 ]	15	60
13	[ 0, 0, 0, 0, 0, 1 ]	15	12
1	[ 0, 0, 0, 0, 0, 0 ]	45	1

Highest weight: [ 0, 0, 0, 0, 1, 2 ]
Characteristic: not 2,3,5,13
Dimension: 3927

Level	dominant weight	weight multiplicity	length of W-orbit
47	[ 0, 0, 0, 0, 1, 2 ]	1	120
45	[ 0, 0, 0, 0, 2, 0 ]	1	60
43	[ 0, 0, 0, 1, 0, 1 ]	2	480
37	[ 0, 0, 1, 0, 0, 0 ]	3	240
37	[ 0, 0, 0, 0, 0, 3 ]	1	12
35	[ 0, 0, 0, 0, 1, 1 ]	2	120
31	[ 0, 0, 0, 1, 0, 0 ]	3	160
25	[ 0, 0, 0, 0, 0, 2 ]	11	12
23	[ 0, 0, 0, 0, 1, 0 ]	16	60
13	[ 0, 0, 0, 0, 0, 1 ]	16	12
1	[ 0, 0, 0, 0, 0, 0 ]	51	1