Weight Multiplicities

Groups of type C5, degree bound 2500

Diagram:

1 > 2 - .. - 5

Overview

Dimension	Highest weight	Characteristic
1	[ 0, 0, 0, 0, 0 ]	all
10	[ 0, 0, 0, 0, 1 ]	all
32	[ 1, 0, 0, 0, 0 ]	2
43	[ 0, 0, 0, 1, 0 ]	5
44	[ 0, 0, 0, 1, 0 ]	not 5
55	[ 0, 0, 0, 0, 2 ]	not 2
100	[ 0, 0, 1, 0, 0 ]	2
110	[ 0, 0, 1, 0, 0 ]	not 2
121	[ 0, 1, 0, 0, 0 ]	3
122	[ 1, 0, 0, 0, 0 ]	3
132	[ 1, 0, 0, 0, 0 ]	not 2, 3
164	[ 0, 1, 0, 0, 0 ]	2
165	[ 0, 1, 0, 0, 0 ]	not 2, 3
210	[ 0, 0, 0, 1, 1 ]	3
220	[ 0, 0, 0, 0, 3 ]	not 2, 3
310	[ 0, 0, 0, 1, 1 ]	11
320	[ 0, 0, 0, 1, 1 ]	not 3, 11
320	[ 1, 0, 0, 0, 1 ]	2
615	[ 0, 0, 0, 2, 0 ]	3
670	[ 0, 0, 1, 0, 1 ]	2
715	[ 0, 0, 0, 0, 4 ]	not 2, 3
779	[ 0, 0, 0, 2, 0 ]	11
780	[ 0, 0, 0, 2, 0 ]	not 2, 3, 11
848	[ 0, 0, 1, 0, 1 ]	5
891	[ 0, 0, 1, 0, 1 ]	not 2, 5
1088	[ 0, 1, 0, 0, 1 ]	3
1099	[ 1, 0, 0, 0, 1 ]	3
1155	[ 1, 0, 0, 0, 1 ]	not 2, 3
1276	[ 0, 1, 0, 0, 1 ]	5
1375	[ 0, 0, 0, 1, 2 ]	3
1408	[ 0, 1, 0, 0, 1 ]	not 3, 5
1408	[ 1, 0, 0, 1, 0 ]	2
1430	[ 0, 0, 0, 1, 2 ]	not 2, 3
1452	[ 0, 0, 1, 1, 0 ]	3
1562	[ 1, 1, 0, 0, 0 ]	5
1563	[ 2, 0, 0, 0, 0 ]	5
1992	[ 0, 0, 0, 1, 3 ]	5
2002	[ 0, 0, 0, 0, 5 ]	not 2, 3, 5

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: all
Dimension: 10

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

Highest weight: [ 1, 0, 0, 0, 0 ]
Characteristic: 2
Dimension: 32

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

Highest weight: [ 0, 0, 0, 1, 0 ]
Characteristic: 5
Dimension: 43

Level	dominant weight	weight multiplicity	length of W-orbit
17	[ 0, 0, 0, 1, 0 ]	1	40
1	[ 0, 0, 0, 0, 0 ]	3	1

Highest weight: [ 0, 0, 0, 1, 0 ]
Characteristic: not 5
Dimension: 44

Level	dominant weight	weight multiplicity	length of W-orbit
17	[ 0, 0, 0, 1, 0 ]	1	40
1	[ 0, 0, 0, 0, 0 ]	4	1

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

Level	dominant weight	weight multiplicity	length of W-orbit
19	[ 0, 0, 0, 0, 2 ]	1	10
17	[ 0, 0, 0, 1, 0 ]	1	40
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
22	[ 0, 0, 1, 0, 0 ]	1	80
10	[ 0, 0, 0, 0, 1 ]	2	10

Highest weight: [ 0, 0, 1, 0, 0 ]
Characteristic: not 2
Dimension: 110

Level	dominant weight	weight multiplicity	length of W-orbit
22	[ 0, 0, 1, 0, 0 ]	1	80
10	[ 0, 0, 0, 0, 1 ]	3	10

Highest weight: [ 0, 1, 0, 0, 0 ]
Characteristic: 3
Dimension: 121

Level	dominant weight	weight multiplicity	length of W-orbit
25	[ 0, 1, 0, 0, 0 ]	1	80
17	[ 0, 0, 0, 1, 0 ]	1	40
1	[ 0, 0, 0, 0, 0 ]	1	1

Highest weight: [ 1, 0, 0, 0, 0 ]
Characteristic: 3
Dimension: 122

Level	dominant weight	weight multiplicity	length of W-orbit
26	[ 1, 0, 0, 0, 0 ]	1	32
22	[ 0, 0, 1, 0, 0 ]	1	80
10	[ 0, 0, 0, 0, 1 ]	1	10

Highest weight: [ 1, 0, 0, 0, 0 ]
Characteristic: not 2,3
Dimension: 132

Level	dominant weight	weight multiplicity	length of W-orbit
26	[ 1, 0, 0, 0, 0 ]	1	32
22	[ 0, 0, 1, 0, 0 ]	1	80
10	[ 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
25	[ 0, 1, 0, 0, 0 ]	1	80
17	[ 0, 0, 0, 1, 0 ]	2	40
1	[ 0, 0, 0, 0, 0 ]	4	1

Highest weight: [ 0, 1, 0, 0, 0 ]
Characteristic: not 2,3
Dimension: 165

Level	dominant weight	weight multiplicity	length of W-orbit
25	[ 0, 1, 0, 0, 0 ]	1	80
17	[ 0, 0, 0, 1, 0 ]	2	40
1	[ 0, 0, 0, 0, 0 ]	5	1

Highest weight: [ 0, 0, 0, 1, 1 ]
Characteristic: 3
Dimension: 210

Level	dominant weight	weight multiplicity	length of W-orbit
26	[ 0, 0, 0, 1, 1 ]	1	80
22	[ 0, 0, 1, 0, 0 ]	1	80
10	[ 0, 0, 0, 0, 1 ]	5	10

Highest weight: [ 0, 0, 0, 0, 3 ]
Characteristic: not 2,3
Dimension: 220

Level	dominant weight	weight multiplicity	length of W-orbit
28	[ 0, 0, 0, 0, 3 ]	1	10
26	[ 0, 0, 0, 1, 1 ]	1	80
22	[ 0, 0, 1, 0, 0 ]	1	80
10	[ 0, 0, 0, 0, 1 ]	5	10

Highest weight: [ 0, 0, 0, 1, 1 ]
Characteristic: 11
Dimension: 310

Level	dominant weight	weight multiplicity	length of W-orbit
26	[ 0, 0, 0, 1, 1 ]	1	80
22	[ 0, 0, 1, 0, 0 ]	2	80
10	[ 0, 0, 0, 0, 1 ]	7	10

Highest weight: [ 0, 0, 0, 1, 1 ]
Characteristic: not 3,11
Dimension: 320

Level	dominant weight	weight multiplicity	length of W-orbit
26	[ 0, 0, 0, 1, 1 ]	1	80
22	[ 0, 0, 1, 0, 0 ]	2	80
10	[ 0, 0, 0, 0, 1 ]	8	10

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

Level	dominant weight	weight multiplicity	length of W-orbit
35	[ 1, 0, 0, 0, 1 ]	1	160
25	[ 0, 1, 0, 0, 0 ]	2	80

Highest weight: [ 0, 0, 0, 2, 0 ]
Characteristic: 3
Dimension: 615

Level	dominant weight	weight multiplicity	length of W-orbit
33	[ 0, 0, 0, 2, 0 ]	1	40
31	[ 0, 0, 1, 0, 1 ]	1	240
25	[ 0, 1, 0, 0, 0 ]	1	80
19	[ 0, 0, 0, 0, 2 ]	4	10
17	[ 0, 0, 0, 1, 0 ]	5	40
1	[ 0, 0, 0, 0, 0 ]	15	1

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

Level	dominant weight	weight multiplicity	length of W-orbit
31	[ 0, 0, 1, 0, 1 ]	1	240
25	[ 0, 1, 0, 0, 0 ]	2	80
19	[ 0, 0, 0, 0, 2 ]	2	10
17	[ 0, 0, 0, 1, 0 ]	6	40
1	[ 0, 0, 0, 0, 0 ]	10	1

Highest weight: [ 0, 0, 0, 0, 4 ]
Characteristic: not 2,3
Dimension: 715

Level	dominant weight	weight multiplicity	length of W-orbit
37	[ 0, 0, 0, 0, 4 ]	1	10
35	[ 0, 0, 0, 1, 2 ]	1	80
33	[ 0, 0, 0, 2, 0 ]	1	40
31	[ 0, 0, 1, 0, 1 ]	1	240
25	[ 0, 1, 0, 0, 0 ]	1	80
19	[ 0, 0, 0, 0, 2 ]	5	10
17	[ 0, 0, 0, 1, 0 ]	5	40
1	[ 0, 0, 0, 0, 0 ]	15	1

Highest weight: [ 0, 0, 0, 2, 0 ]
Characteristic: 11
Dimension: 779

Level	dominant weight	weight multiplicity	length of W-orbit
33	[ 0, 0, 0, 2, 0 ]	1	40
31	[ 0, 0, 1, 0, 1 ]	1	240
25	[ 0, 1, 0, 0, 0 ]	2	80
19	[ 0, 0, 0, 0, 2 ]	4	10
17	[ 0, 0, 0, 1, 0 ]	7	40
1	[ 0, 0, 0, 0, 0 ]	19	1

Highest weight: [ 0, 0, 0, 2, 0 ]
Characteristic: not 2,3,11
Dimension: 780

Level	dominant weight	weight multiplicity	length of W-orbit
33	[ 0, 0, 0, 2, 0 ]	1	40
31	[ 0, 0, 1, 0, 1 ]	1	240
25	[ 0, 1, 0, 0, 0 ]	2	80
19	[ 0, 0, 0, 0, 2 ]	4	10
17	[ 0, 0, 0, 1, 0 ]	7	40
1	[ 0, 0, 0, 0, 0 ]	20	1

Highest weight: [ 0, 0, 1, 0, 1 ]
Characteristic: 5
Dimension: 848

Level	dominant weight	weight multiplicity	length of W-orbit
31	[ 0, 0, 1, 0, 1 ]	1	240
25	[ 0, 1, 0, 0, 0 ]	3	80
19	[ 0, 0, 0, 0, 2 ]	3	10
17	[ 0, 0, 0, 1, 0 ]	8	40
1	[ 0, 0, 0, 0, 0 ]	18	1

Highest weight: [ 0, 0, 1, 0, 1 ]
Characteristic: not 2,5
Dimension: 891

Level	dominant weight	weight multiplicity	length of W-orbit
31	[ 0, 0, 1, 0, 1 ]	1	240
25	[ 0, 1, 0, 0, 0 ]	3	80
19	[ 0, 0, 0, 0, 2 ]	3	10
17	[ 0, 0, 0, 1, 0 ]	9	40
1	[ 0, 0, 0, 0, 0 ]	21	1

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

Level	dominant weight	weight multiplicity	length of W-orbit
34	[ 0, 1, 0, 0, 1 ]	1	320
26	[ 1, 0, 0, 0, 0 ]	4	32
26	[ 0, 0, 0, 1, 1 ]	1	80
22	[ 0, 0, 1, 0, 0 ]	6	80
10	[ 0, 0, 0, 0, 1 ]	8	10

Highest weight: [ 1, 0, 0, 0, 1 ]
Characteristic: 3
Dimension: 1099

Level	dominant weight	weight multiplicity	length of W-orbit
35	[ 1, 0, 0, 0, 1 ]	1	160
31	[ 0, 0, 1, 0, 1 ]	1	240
25	[ 0, 1, 0, 0, 0 ]	5	80
19	[ 0, 0, 0, 0, 2 ]	1	10
17	[ 0, 0, 0, 1, 0 ]	7	40
1	[ 0, 0, 0, 0, 0 ]	9	1

Highest weight: [ 1, 0, 0, 0, 1 ]
Characteristic: not 2,3
Dimension: 1155

Level	dominant weight	weight multiplicity	length of W-orbit
35	[ 1, 0, 0, 0, 1 ]	1	160
31	[ 0, 0, 1, 0, 1 ]	1	240
25	[ 0, 1, 0, 0, 0 ]	5	80
19	[ 0, 0, 0, 0, 2 ]	2	10
17	[ 0, 0, 0, 1, 0 ]	8	40
1	[ 0, 0, 0, 0, 0 ]	15	1

Highest weight: [ 0, 1, 0, 0, 1 ]
Characteristic: 5
Dimension: 1276

Level	dominant weight	weight multiplicity	length of W-orbit
34	[ 0, 1, 0, 0, 1 ]	1	320
26	[ 1, 0, 0, 0, 0 ]	3	32
26	[ 0, 0, 0, 1, 1 ]	2	80
22	[ 0, 0, 1, 0, 0 ]	7	80
10	[ 0, 0, 0, 0, 1 ]	14	10

Highest weight: [ 0, 0, 0, 1, 2 ]
Characteristic: 3
Dimension: 1375

Level	dominant weight	weight multiplicity	length of W-orbit
35	[ 0, 0, 0, 1, 2 ]	1	80
33	[ 0, 0, 0, 2, 0 ]	1	40
31	[ 0, 0, 1, 0, 1 ]	2	240
25	[ 0, 1, 0, 0, 0 ]	3	80
19	[ 0, 0, 0, 0, 2 ]	7	10
17	[ 0, 0, 0, 1, 0 ]	11	40
1	[ 0, 0, 0, 0, 0 ]	25	1

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

Level	dominant weight	weight multiplicity	length of W-orbit
34	[ 0, 1, 0, 0, 1 ]	1	320
26	[ 1, 0, 0, 0, 0 ]	4	32
26	[ 0, 0, 0, 1, 1 ]	2	80
22	[ 0, 0, 1, 0, 0 ]	8	80
10	[ 0, 0, 0, 0, 1 ]	16	10

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

Level	dominant weight	weight multiplicity	length of W-orbit
42	[ 1, 0, 0, 1, 0 ]	1	320
34	[ 0, 1, 0, 0, 1 ]	2	320
26	[ 1, 0, 0, 0, 0 ]	4	32
22	[ 0, 0, 1, 0, 0 ]	4	80

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

Level	dominant weight	weight multiplicity	length of W-orbit
35	[ 0, 0, 0, 1, 2 ]	1	80
33	[ 0, 0, 0, 2, 0 ]	1	40
31	[ 0, 0, 1, 0, 1 ]	2	240
25	[ 0, 1, 0, 0, 0 ]	3	80
19	[ 0, 0, 0, 0, 2 ]	8	10
17	[ 0, 0, 0, 1, 0 ]	12	40
1	[ 0, 0, 0, 0, 0 ]	30	1

Highest weight: [ 0, 0, 1, 1, 0 ]
Characteristic: 3
Dimension: 1452

Level	dominant weight	weight multiplicity	length of W-orbit
38	[ 0, 0, 1, 1, 0 ]	1	240
34	[ 0, 1, 0, 0, 1 ]	1	320
26	[ 1, 0, 0, 0, 0 ]	1	32
26	[ 0, 0, 0, 1, 1 ]	4	80
22	[ 0, 0, 1, 0, 0 ]	5	80
10	[ 0, 0, 0, 0, 1 ]	14	10

Highest weight: [ 1, 1, 0, 0, 0 ]
Characteristic: 5
Dimension: 1562

Level	dominant weight	weight multiplicity	length of W-orbit
50	[ 1, 1, 0, 0, 0 ]	1	160
46	[ 0, 1, 1, 0, 0 ]	1	320
42	[ 1, 0, 0, 1, 0 ]	1	320
38	[ 0, 0, 1, 1, 0 ]	1	240
34	[ 0, 1, 0, 0, 1 ]	1	320
26	[ 1, 0, 0, 0, 0 ]	1	32
26	[ 0, 0, 0, 1, 1 ]	1	80
22	[ 0, 0, 1, 0, 0 ]	1	80
10	[ 0, 0, 0, 0, 1 ]	1	10

Highest weight: [ 2, 0, 0, 0, 0 ]
Characteristic: 5
Dimension: 1563

Level	dominant weight	weight multiplicity	length of W-orbit
51	[ 2, 0, 0, 0, 0 ]	1	32
49	[ 0, 2, 0, 0, 0 ]	1	80
47	[ 1, 0, 1, 0, 0 ]	1	320
43	[ 0, 0, 2, 0, 0 ]	1	80
41	[ 0, 1, 0, 1, 0 ]	1	480
35	[ 1, 0, 0, 0, 1 ]	1	160
33	[ 0, 0, 0, 2, 0 ]	1	40
31	[ 0, 0, 1, 0, 1 ]	1	240
25	[ 0, 1, 0, 0, 0 ]	1	80
19	[ 0, 0, 0, 0, 2 ]	1	10
17	[ 0, 0, 0, 1, 0 ]	1	40
1	[ 0, 0, 0, 0, 0 ]	1	1

Highest weight: [ 0, 0, 0, 1, 3 ]
Characteristic: 5
Dimension: 1992

Level	dominant weight	weight multiplicity	length of W-orbit
44	[ 0, 0, 0, 1, 3 ]	1	80
42	[ 0, 0, 0, 2, 1 ]	1	80
40	[ 0, 0, 1, 0, 2 ]	1	240
38	[ 0, 0, 1, 1, 0 ]	1	240
34	[ 0, 1, 0, 0, 1 ]	1	320
28	[ 0, 0, 0, 0, 3 ]	5	10
26	[ 1, 0, 0, 0, 0 ]	1	32
26	[ 0, 0, 0, 1, 1 ]	5	80
22	[ 0, 0, 1, 0, 0 ]	5	80
10	[ 0, 0, 0, 0, 1 ]	15	10

Highest weight: [ 0, 0, 0, 0, 5 ]
Characteristic: not 2,3,5
Dimension: 2002

Level	dominant weight	weight multiplicity	length of W-orbit
46	[ 0, 0, 0, 0, 5 ]	1	10
44	[ 0, 0, 0, 1, 3 ]	1	80
42	[ 0, 0, 0, 2, 1 ]	1	80
40	[ 0, 0, 1, 0, 2 ]	1	240
38	[ 0, 0, 1, 1, 0 ]	1	240
34	[ 0, 1, 0, 0, 1 ]	1	320
28	[ 0, 0, 0, 0, 3 ]	5	10
26	[ 1, 0, 0, 0, 0 ]	1	32
26	[ 0, 0, 0, 1, 1 ]	5	80
22	[ 0, 0, 1, 0, 0 ]	5	80
10	[ 0, 0, 0, 0, 1 ]	15	10