Weight Multiplicities

Groups of type B5, degree bound 2000

Diagram:

1 < 2 - .. - 5

Overview

Dimension	Highest weight	Characteristic
1	[ 0, 0, 0, 0, 0 ]	all
10	[ 0, 0, 0, 0, 1 ]	2
11	[ 0, 0, 0, 0, 1 ]	not 2
32	[ 1, 0, 0, 0, 0 ]	all
44	[ 0, 0, 0, 1, 0 ]	2
55	[ 0, 0, 0, 1, 0 ]	not 2
64	[ 0, 0, 0, 0, 2 ]	11
65	[ 0, 0, 0, 0, 2 ]	not 2, 11
100	[ 0, 0, 1, 0, 0 ]	2
164	[ 0, 1, 0, 0, 0 ]	2
165	[ 0, 0, 1, 0, 0 ]	not 2
264	[ 0, 0, 0, 0, 3 ]	13
264	[ 0, 0, 0, 1, 1 ]	3
275	[ 0, 0, 0, 0, 3 ]	not 2, 3, 13
288	[ 1, 0, 0, 0, 1 ]	11
320	[ 0, 0, 0, 1, 1 ]	2
320	[ 1, 0, 0, 0, 1 ]	not 11
330	[ 0, 1, 0, 0, 0 ]	not 2
418	[ 0, 0, 0, 1, 1 ]	5
429	[ 0, 0, 0, 1, 1 ]	not 2, 3, 5
462	[ 2, 0, 0, 0, 0 ]	not 2
670	[ 0, 0, 1, 0, 1 ]	2
749	[ 0, 0, 0, 2, 0 ]	3
870	[ 0, 0, 0, 0, 4 ]	5
934	[ 0, 0, 0, 0, 4 ]	13
935	[ 0, 0, 0, 0, 4 ]	not 2, 3, 5, 13
1088	[ 1, 0, 0, 1, 0 ]	3
1143	[ 0, 0, 0, 2, 0 ]	5
1144	[ 0, 0, 0, 2, 0 ]	not 2, 3, 5
1375	[ 0, 0, 1, 0, 1 ]	3
1376	[ 1, 0, 0, 1, 0 ]	5
1408	[ 0, 1, 0, 0, 1 ]	2
1408	[ 1, 0, 0, 1, 0 ]	not 3, 5
1430	[ 0, 0, 1, 0, 1 ]	not 2, 3
1440	[ 1, 0, 0, 0, 2 ]	13
1760	[ 1, 0, 0, 0, 2 ]	not 2, 13
1760	[ 1, 1, 0, 0, 0 ]	5
1961	[ 0, 0, 0, 1, 2 ]	11
1970	[ 0, 0, 0, 1, 2 ]	13
1991	[ 0, 0, 1, 1, 0 ]	3

The characters

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

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

Highest weight: [ 0, 0, 0, 0, 1 ]
Characteristic: 2
Dimension: 10

Level	dominant weight	weight multiplicity	length of W-orbit
11	[ 0, 0, 0, 0, 1 ]	1	10

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

Level	dominant weight	weight multiplicity	length of W-orbit
11	[ 0, 0, 0, 0, 1 ]	1	10
1	[ 0, 0, 0, 0, 0 ]	1	1

Highest weight: [ 1, 0, 0, 0, 0 ]
Characteristic: all
Dimension: 32

Level	dominant weight	weight multiplicity	length of W-orbit
16	[ 1, 0, 0, 0, 0 ]	1	32

Highest weight: [ 0, 0, 0, 1, 0 ]
Characteristic: 2
Dimension: 44

Level	dominant weight	weight multiplicity	length of W-orbit
19	[ 0, 0, 0, 1, 0 ]	1	40
1	[ 0, 0, 0, 0, 0 ]	4	1

Highest weight: [ 0, 0, 0, 1, 0 ]
Characteristic: not 2
Dimension: 55

Level	dominant weight	weight multiplicity	length of W-orbit
19	[ 0, 0, 0, 1, 0 ]	1	40
11	[ 0, 0, 0, 0, 1 ]	1	10
1	[ 0, 0, 0, 0, 0 ]	5	1

Highest weight: [ 0, 0, 0, 0, 2 ]
Characteristic: 11
Dimension: 64

Level	dominant weight	weight multiplicity	length of W-orbit
21	[ 0, 0, 0, 0, 2 ]	1	10
19	[ 0, 0, 0, 1, 0 ]	1	40
11	[ 0, 0, 0, 0, 1 ]	1	10
1	[ 0, 0, 0, 0, 0 ]	4	1

Highest weight: [ 0, 0, 0, 0, 2 ]
Characteristic: not 2,11
Dimension: 65

Level	dominant weight	weight multiplicity	length of W-orbit
21	[ 0, 0, 0, 0, 2 ]	1	10
19	[ 0, 0, 0, 1, 0 ]	1	40
11	[ 0, 0, 0, 0, 1 ]	1	10
1	[ 0, 0, 0, 0, 0 ]	5	1

Highest weight: [ 0, 0, 1, 0, 0 ]
Characteristic: 2
Dimension: 100

Level	dominant weight	weight multiplicity	length of W-orbit
25	[ 0, 0, 1, 0, 0 ]	1	80
11	[ 0, 0, 0, 0, 1 ]	2	10

Highest weight: [ 0, 1, 0, 0, 0 ]
Characteristic: 2
Dimension: 164

Level	dominant weight	weight multiplicity	length of W-orbit
29	[ 0, 1, 0, 0, 0 ]	1	80
19	[ 0, 0, 0, 1, 0 ]	2	40
1	[ 0, 0, 0, 0, 0 ]	4	1

Highest weight: [ 0, 0, 1, 0, 0 ]
Characteristic: not 2
Dimension: 165

Level	dominant weight	weight multiplicity	length of W-orbit
25	[ 0, 0, 1, 0, 0 ]	1	80
19	[ 0, 0, 0, 1, 0 ]	1	40
11	[ 0, 0, 0, 0, 1 ]	4	10
1	[ 0, 0, 0, 0, 0 ]	5	1

Highest weight: [ 0, 0, 0, 0, 3 ]
Characteristic: 13
Dimension: 264

Level	dominant weight	weight multiplicity	length of W-orbit
31	[ 0, 0, 0, 0, 3 ]	1	10
29	[ 0, 0, 0, 1, 1 ]	1	80
25	[ 0, 0, 1, 0, 0 ]	1	80
21	[ 0, 0, 0, 0, 2 ]	1	10
19	[ 0, 0, 0, 1, 0 ]	1	40
11	[ 0, 0, 0, 0, 1 ]	4	10
1	[ 0, 0, 0, 0, 0 ]	4	1

Highest weight: [ 0, 0, 0, 1, 1 ]
Characteristic: 3
Dimension: 264

Level	dominant weight	weight multiplicity	length of W-orbit
29	[ 0, 0, 0, 1, 1 ]	1	80
25	[ 0, 0, 1, 0, 0 ]	1	80
21	[ 0, 0, 0, 0, 2 ]	1	10
19	[ 0, 0, 0, 1, 0 ]	1	40
11	[ 0, 0, 0, 0, 1 ]	5	10
1	[ 0, 0, 0, 0, 0 ]	4	1

Highest weight: [ 0, 0, 0, 0, 3 ]
Characteristic: not 2,3,13
Dimension: 275

Level	dominant weight	weight multiplicity	length of W-orbit
31	[ 0, 0, 0, 0, 3 ]	1	10
29	[ 0, 0, 0, 1, 1 ]	1	80
25	[ 0, 0, 1, 0, 0 ]	1	80
21	[ 0, 0, 0, 0, 2 ]	1	10
19	[ 0, 0, 0, 1, 0 ]	1	40
11	[ 0, 0, 0, 0, 1 ]	5	10
1	[ 0, 0, 0, 0, 0 ]	5	1

Highest weight: [ 1, 0, 0, 0, 1 ]
Characteristic: 11
Dimension: 288

Level	dominant weight	weight multiplicity	length of W-orbit
26	[ 1, 0, 0, 0, 1 ]	1	160
16	[ 1, 0, 0, 0, 0 ]	4	32

Highest weight: [ 0, 0, 0, 1, 1 ]
Characteristic: 2
Dimension: 320

Level	dominant weight	weight multiplicity	length of W-orbit
29	[ 0, 0, 0, 1, 1 ]	1	80
25	[ 0, 0, 1, 0, 0 ]	2	80
11	[ 0, 0, 0, 0, 1 ]	8	10

Highest weight: [ 1, 0, 0, 0, 1 ]
Characteristic: not 11
Dimension: 320

Level	dominant weight	weight multiplicity	length of W-orbit
26	[ 1, 0, 0, 0, 1 ]	1	160
16	[ 1, 0, 0, 0, 0 ]	5	32

Highest weight: [ 0, 1, 0, 0, 0 ]
Characteristic: not 2
Dimension: 330

Level	dominant weight	weight multiplicity	length of W-orbit
29	[ 0, 1, 0, 0, 0 ]	1	80
25	[ 0, 0, 1, 0, 0 ]	1	80
19	[ 0, 0, 0, 1, 0 ]	3	40
11	[ 0, 0, 0, 0, 1 ]	4	10
1	[ 0, 0, 0, 0, 0 ]	10	1

Highest weight: [ 0, 0, 0, 1, 1 ]
Characteristic: 5
Dimension: 418

Level	dominant weight	weight multiplicity	length of W-orbit
29	[ 0, 0, 0, 1, 1 ]	1	80
25	[ 0, 0, 1, 0, 0 ]	2	80
21	[ 0, 0, 0, 0, 2 ]	1	10
19	[ 0, 0, 0, 1, 0 ]	2	40
11	[ 0, 0, 0, 0, 1 ]	8	10
1	[ 0, 0, 0, 0, 0 ]	8	1

Highest weight: [ 0, 0, 0, 1, 1 ]
Characteristic: not 2,3,5
Dimension: 429

Level	dominant weight	weight multiplicity	length of W-orbit
29	[ 0, 0, 0, 1, 1 ]	1	80
25	[ 0, 0, 1, 0, 0 ]	2	80
21	[ 0, 0, 0, 0, 2 ]	1	10
19	[ 0, 0, 0, 1, 0 ]	2	40
11	[ 0, 0, 0, 0, 1 ]	9	10
1	[ 0, 0, 0, 0, 0 ]	9	1

Highest weight: [ 2, 0, 0, 0, 0 ]
Characteristic: not 2
Dimension: 462

Level	dominant weight	weight multiplicity	length of W-orbit
31	[ 2, 0, 0, 0, 0 ]	1	32
29	[ 0, 1, 0, 0, 0 ]	1	80
25	[ 0, 0, 1, 0, 0 ]	2	80
19	[ 0, 0, 0, 1, 0 ]	3	40
11	[ 0, 0, 0, 0, 1 ]	6	10
1	[ 0, 0, 0, 0, 0 ]	10	1

Highest weight: [ 0, 0, 1, 0, 1 ]
Characteristic: 2
Dimension: 670

Level	dominant weight	weight multiplicity	length of W-orbit
35	[ 0, 0, 1, 0, 1 ]	1	240
29	[ 0, 1, 0, 0, 0 ]	2	80
21	[ 0, 0, 0, 0, 2 ]	2	10
19	[ 0, 0, 0, 1, 0 ]	6	40
1	[ 0, 0, 0, 0, 0 ]	10	1

Highest weight: [ 0, 0, 0, 2, 0 ]
Characteristic: 3
Dimension: 749

Level	dominant weight	weight multiplicity	length of W-orbit
37	[ 0, 0, 0, 2, 0 ]	1	40
35	[ 0, 0, 1, 0, 1 ]	1	240
29	[ 0, 1, 0, 0, 0 ]	1	80
29	[ 0, 0, 0, 1, 1 ]	1	80
25	[ 0, 0, 1, 0, 0 ]	1	80
21	[ 0, 0, 0, 0, 2 ]	3	10
19	[ 0, 0, 0, 1, 0 ]	4	40
11	[ 0, 0, 0, 0, 1 ]	3	10
1	[ 0, 0, 0, 0, 0 ]	9	1

Highest weight: [ 0, 0, 0, 0, 4 ]
Characteristic: 5
Dimension: 870

Level	dominant weight	weight multiplicity	length of W-orbit
41	[ 0, 0, 0, 0, 4 ]	1	10
39	[ 0, 0, 0, 1, 2 ]	1	80
37	[ 0, 0, 0, 2, 0 ]	1	40
35	[ 0, 0, 1, 0, 1 ]	1	240
31	[ 0, 0, 0, 0, 3 ]	1	10
29	[ 0, 1, 0, 0, 0 ]	1	80
29	[ 0, 0, 0, 1, 1 ]	1	80
25	[ 0, 0, 1, 0, 0 ]	1	80
21	[ 0, 0, 0, 0, 2 ]	4	10
19	[ 0, 0, 0, 1, 0 ]	4	40
11	[ 0, 0, 0, 0, 1 ]	4	10
1	[ 0, 0, 0, 0, 0 ]	10	1

Highest weight: [ 0, 0, 0, 0, 4 ]
Characteristic: 13
Dimension: 934

Level	dominant weight	weight multiplicity	length of W-orbit
41	[ 0, 0, 0, 0, 4 ]	1	10
39	[ 0, 0, 0, 1, 2 ]	1	80
37	[ 0, 0, 0, 2, 0 ]	1	40
35	[ 0, 0, 1, 0, 1 ]	1	240
31	[ 0, 0, 0, 0, 3 ]	1	10
29	[ 0, 1, 0, 0, 0 ]	1	80
29	[ 0, 0, 0, 1, 1 ]	1	80
25	[ 0, 0, 1, 0, 0 ]	1	80
21	[ 0, 0, 0, 0, 2 ]	5	10
19	[ 0, 0, 0, 1, 0 ]	5	40
11	[ 0, 0, 0, 0, 1 ]	5	10
1	[ 0, 0, 0, 0, 0 ]	14	1

Highest weight: [ 0, 0, 0, 0, 4 ]
Characteristic: not 2,3,5,13
Dimension: 935

Level	dominant weight	weight multiplicity	length of W-orbit
41	[ 0, 0, 0, 0, 4 ]	1	10
39	[ 0, 0, 0, 1, 2 ]	1	80
37	[ 0, 0, 0, 2, 0 ]	1	40
35	[ 0, 0, 1, 0, 1 ]	1	240
31	[ 0, 0, 0, 0, 3 ]	1	10
29	[ 0, 1, 0, 0, 0 ]	1	80
29	[ 0, 0, 0, 1, 1 ]	1	80
25	[ 0, 0, 1, 0, 0 ]	1	80
21	[ 0, 0, 0, 0, 2 ]	5	10
19	[ 0, 0, 0, 1, 0 ]	5	40
11	[ 0, 0, 0, 0, 1 ]	5	10
1	[ 0, 0, 0, 0, 0 ]	15	1

Highest weight: [ 1, 0, 0, 1, 0 ]
Characteristic: 3
Dimension: 1088

Level	dominant weight	weight multiplicity	length of W-orbit
34	[ 1, 0, 0, 1, 0 ]	1	320
26	[ 1, 0, 0, 0, 1 ]	3	160
16	[ 1, 0, 0, 0, 0 ]	9	32

Highest weight: [ 0, 0, 0, 2, 0 ]
Characteristic: 5
Dimension: 1143

Level	dominant weight	weight multiplicity	length of W-orbit
37	[ 0, 0, 0, 2, 0 ]	1	40
35	[ 0, 0, 1, 0, 1 ]	1	240
29	[ 0, 1, 0, 0, 0 ]	2	80
29	[ 0, 0, 0, 1, 1 ]	1	80
25	[ 0, 0, 1, 0, 0 ]	2	80
21	[ 0, 0, 0, 0, 2 ]	4	10
19	[ 0, 0, 0, 1, 0 ]	8	40
11	[ 0, 0, 0, 0, 1 ]	8	10
1	[ 0, 0, 0, 0, 0 ]	23	1

Highest weight: [ 0, 0, 0, 2, 0 ]
Characteristic: not 2,3,5
Dimension: 1144

Level	dominant weight	weight multiplicity	length of W-orbit
37	[ 0, 0, 0, 2, 0 ]	1	40
35	[ 0, 0, 1, 0, 1 ]	1	240
29	[ 0, 1, 0, 0, 0 ]	2	80
29	[ 0, 0, 0, 1, 1 ]	1	80
25	[ 0, 0, 1, 0, 0 ]	2	80
21	[ 0, 0, 0, 0, 2 ]	4	10
19	[ 0, 0, 0, 1, 0 ]	8	40
11	[ 0, 0, 0, 0, 1 ]	8	10
1	[ 0, 0, 0, 0, 0 ]	24	1

Highest weight: [ 0, 0, 1, 0, 1 ]
Characteristic: 3
Dimension: 1375

Level	dominant weight	weight multiplicity	length of W-orbit
35	[ 0, 0, 1, 0, 1 ]	1	240
29	[ 0, 1, 0, 0, 0 ]	3	80
29	[ 0, 0, 0, 1, 1 ]	1	80
25	[ 0, 0, 1, 0, 0 ]	3	80
21	[ 0, 0, 0, 0, 2 ]	4	10
19	[ 0, 0, 0, 1, 0 ]	10	40
11	[ 0, 0, 0, 0, 1 ]	11	10
1	[ 0, 0, 0, 0, 0 ]	25	1

Highest weight: [ 1, 0, 0, 1, 0 ]
Characteristic: 5
Dimension: 1376

Level	dominant weight	weight multiplicity	length of W-orbit
34	[ 1, 0, 0, 1, 0 ]	1	320
26	[ 1, 0, 0, 0, 1 ]	4	160
16	[ 1, 0, 0, 0, 0 ]	13	32

Highest weight: [ 0, 1, 0, 0, 1 ]
Characteristic: 2
Dimension: 1408

Level	dominant weight	weight multiplicity	length of W-orbit
39	[ 0, 1, 0, 0, 1 ]	1	320
31	[ 2, 0, 0, 0, 0 ]	4	32
29	[ 0, 0, 0, 1, 1 ]	2	80
25	[ 0, 0, 1, 0, 0 ]	8	80
11	[ 0, 0, 0, 0, 1 ]	16	10

Highest weight: [ 1, 0, 0, 1, 0 ]
Characteristic: not 3,5
Dimension: 1408

Level	dominant weight	weight multiplicity	length of W-orbit
34	[ 1, 0, 0, 1, 0 ]	1	320
26	[ 1, 0, 0, 0, 1 ]	4	160
16	[ 1, 0, 0, 0, 0 ]	14	32

Highest weight: [ 0, 0, 1, 0, 1 ]
Characteristic: not 2,3
Dimension: 1430

Level	dominant weight	weight multiplicity	length of W-orbit
35	[ 0, 0, 1, 0, 1 ]	1	240
29	[ 0, 1, 0, 0, 0 ]	3	80
29	[ 0, 0, 0, 1, 1 ]	1	80
25	[ 0, 0, 1, 0, 0 ]	3	80
21	[ 0, 0, 0, 0, 2 ]	4	10
19	[ 0, 0, 0, 1, 0 ]	11	40
11	[ 0, 0, 0, 0, 1 ]	12	10
1	[ 0, 0, 0, 0, 0 ]	30	1

Highest weight: [ 1, 0, 0, 0, 2 ]
Characteristic: 13
Dimension: 1440

Level	dominant weight	weight multiplicity	length of W-orbit
36	[ 1, 0, 0, 0, 2 ]	1	160
34	[ 1, 0, 0, 1, 0 ]	1	320
26	[ 1, 0, 0, 0, 1 ]	4	160
16	[ 1, 0, 0, 0, 0 ]	10	32

Highest weight: [ 1, 0, 0, 0, 2 ]
Characteristic: not 2,13
Dimension: 1760

Level	dominant weight	weight multiplicity	length of W-orbit
36	[ 1, 0, 0, 0, 2 ]	1	160
34	[ 1, 0, 0, 1, 0 ]	1	320
26	[ 1, 0, 0, 0, 1 ]	5	160
16	[ 1, 0, 0, 0, 0 ]	15	32

Highest weight: [ 1, 1, 0, 0, 0 ]
Characteristic: 5
Dimension: 1760

Level	dominant weight	weight multiplicity	length of W-orbit
44	[ 1, 1, 0, 0, 0 ]	1	160
40	[ 1, 0, 1, 0, 0 ]	1	320
34	[ 1, 0, 0, 1, 0 ]	2	320
26	[ 1, 0, 0, 0, 1 ]	3	160
16	[ 1, 0, 0, 0, 0 ]	5	32

Highest weight: [ 0, 0, 0, 1, 2 ]
Characteristic: 11
Dimension: 1961

Level	dominant weight	weight multiplicity	length of W-orbit
39	[ 0, 0, 0, 1, 2 ]	1	80
37	[ 0, 0, 0, 2, 0 ]	1	40
35	[ 0, 0, 1, 0, 1 ]	2	240
31	[ 0, 0, 0, 0, 3 ]	1	10
29	[ 0, 1, 0, 0, 0 ]	3	80
29	[ 0, 0, 0, 1, 1 ]	2	80
25	[ 0, 0, 1, 0, 0 ]	3	80
21	[ 0, 0, 0, 0, 2 ]	8	10
19	[ 0, 0, 0, 1, 0 ]	12	40
11	[ 0, 0, 0, 0, 1 ]	12	10
1	[ 0, 0, 0, 0, 0 ]	31	1

Highest weight: [ 0, 0, 0, 1, 2 ]
Characteristic: 13
Dimension: 1970

Level	dominant weight	weight multiplicity	length of W-orbit
39	[ 0, 0, 0, 1, 2 ]	1	80
37	[ 0, 0, 0, 2, 0 ]	1	40
35	[ 0, 0, 1, 0, 1 ]	2	240
31	[ 0, 0, 0, 0, 3 ]	1	10
29	[ 0, 1, 0, 0, 0 ]	3	80
29	[ 0, 0, 0, 1, 1 ]	2	80
25	[ 0, 0, 1, 0, 0 ]	3	80
21	[ 0, 0, 0, 0, 2 ]	9	10
19	[ 0, 0, 0, 1, 0 ]	12	40
11	[ 0, 0, 0, 0, 1 ]	12	10
1	[ 0, 0, 0, 0, 0 ]	30	1

Highest weight: [ 0, 0, 1, 1, 0 ]
Characteristic: 3
Dimension: 1991

Level	dominant weight	weight multiplicity	length of W-orbit
43	[ 0, 0, 1, 1, 0 ]	1	240
39	[ 0, 1, 0, 0, 1 ]	1	320
37	[ 0, 0, 0, 2, 0 ]	1	40
35	[ 0, 0, 1, 0, 1 ]	1	240
31	[ 2, 0, 0, 0, 0 ]	1	32
29	[ 0, 1, 0, 0, 0 ]	1	80
29	[ 0, 0, 0, 1, 1 ]	4	80
25	[ 0, 0, 1, 0, 0 ]	5	80
21	[ 0, 0, 0, 0, 2 ]	3	10
19	[ 0, 0, 0, 1, 0 ]	4	40
11	[ 0, 0, 0, 0, 1 ]	12	10
1	[ 0, 0, 0, 0, 0 ]	9	1