Weight Multiplicities

Groups of type C6, 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 ]	all
64	[ 0, 0, 0, 0, 1, 0 ]	2
64	[ 0, 0, 0, 0, 1, 0 ]	3
64	[ 1, 0, 0, 0, 0, 0 ]	2
65	[ 0, 0, 0, 0, 1, 0 ]	not 2, 3
78	[ 0, 0, 0, 0, 0, 2 ]	not 2
196	[ 0, 0, 0, 1, 0, 0 ]	5
208	[ 0, 0, 0, 1, 0, 0 ]	not 5
352	[ 0, 0, 0, 0, 1, 1 ]	3
364	[ 0, 0, 0, 0, 0, 3 ]	not 2, 3
364	[ 0, 0, 1, 0, 0, 0 ]	2
364	[ 0, 1, 0, 0, 0, 0 ]	3
365	[ 1, 0, 0, 0, 0, 0 ]	3
428	[ 0, 0, 1, 0, 0, 0 ]	5
429	[ 0, 0, 1, 0, 0, 0 ]	not 2, 5
429	[ 1, 0, 0, 0, 0, 0 ]	not 2, 3
548	[ 0, 0, 0, 0, 1, 1 ]	13
560	[ 0, 0, 0, 0, 1, 1 ]	not 3, 13
560	[ 0, 1, 0, 0, 0, 0 ]	2
572	[ 0, 1, 0, 0, 0, 0 ]	not 2, 3
768	[ 1, 0, 0, 0, 0, 1 ]	2
1221	[ 0, 0, 0, 0, 2, 0 ]	3
1365	[ 0, 0, 0, 0, 0, 4 ]	not 2, 3
1508	[ 0, 0, 0, 1, 0, 1 ]	2
1585	[ 0, 0, 0, 0, 2, 0 ]	7
1649	[ 0, 0, 0, 0, 2, 0 ]	13
1650	[ 0, 0, 0, 0, 2, 0 ]	not 2, 3, 7, 13
1924	[ 0, 0, 0, 1, 0, 1 ]	5
1938	[ 0, 0, 0, 1, 0, 1 ]	3
2002	[ 0, 0, 0, 1, 0, 1 ]	not 2, 3, 5
2847	[ 0, 0, 0, 0, 1, 2 ]	7
2925	[ 0, 0, 0, 0, 1, 2 ]	not 2, 7
3432	[ 0, 0, 0, 1, 1, 0 ]	3
3638	[ 0, 1, 0, 0, 0, 1 ]	3
3652	[ 1, 0, 0, 0, 0, 1 ]	3
3796	[ 0, 0, 1, 0, 0, 1 ]	5
3808	[ 0, 0, 1, 0, 0, 1 ]	2

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: all
Dimension: 12

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

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

Level	dominant weight	weight multiplicity	length of W-orbit
21	[ 0, 0, 0, 0, 1, 0 ]	1	60
1	[ 0, 0, 0, 0, 0, 0 ]	4	1

Highest weight: [ 0, 0, 0, 0, 1, 0 ]
Characteristic: 3
Dimension: 64

Level	dominant weight	weight multiplicity	length of W-orbit
21	[ 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: 2
Dimension: 64

Level	dominant weight	weight multiplicity	length of W-orbit
37	[ 1, 0, 0, 0, 0, 0 ]	1	64

Highest weight: [ 0, 0, 0, 0, 1, 0 ]
Characteristic: not 2,3
Dimension: 65

Level	dominant weight	weight multiplicity	length of W-orbit
21	[ 0, 0, 0, 0, 1, 0 ]	1	60
1	[ 0, 0, 0, 0, 0, 0 ]	5	1

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

Level	dominant weight	weight multiplicity	length of W-orbit
23	[ 0, 0, 0, 0, 0, 2 ]	1	12
21	[ 0, 0, 0, 0, 1, 0 ]	1	60
1	[ 0, 0, 0, 0, 0, 0 ]	6	1

Highest weight: [ 0, 0, 0, 1, 0, 0 ]
Characteristic: 5
Dimension: 196

Level	dominant weight	weight multiplicity	length of W-orbit
28	[ 0, 0, 0, 1, 0, 0 ]	1	160
12	[ 0, 0, 0, 0, 0, 1 ]	3	12

Highest weight: [ 0, 0, 0, 1, 0, 0 ]
Characteristic: not 5
Dimension: 208

Level	dominant weight	weight multiplicity	length of W-orbit
28	[ 0, 0, 0, 1, 0, 0 ]	1	160
12	[ 0, 0, 0, 0, 0, 1 ]	4	12

Highest weight: [ 0, 0, 0, 0, 1, 1 ]
Characteristic: 3
Dimension: 352

Level	dominant weight	weight multiplicity	length of W-orbit
32	[ 0, 0, 0, 0, 1, 1 ]	1	120
28	[ 0, 0, 0, 1, 0, 0 ]	1	160
12	[ 0, 0, 0, 0, 0, 1 ]	6	12

Highest weight: [ 0, 0, 0, 0, 0, 3 ]
Characteristic: not 2,3
Dimension: 364

Level	dominant weight	weight multiplicity	length of W-orbit
34	[ 0, 0, 0, 0, 0, 3 ]	1	12
32	[ 0, 0, 0, 0, 1, 1 ]	1	120
28	[ 0, 0, 0, 1, 0, 0 ]	1	160
12	[ 0, 0, 0, 0, 0, 1 ]	6	12

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

Level	dominant weight	weight multiplicity	length of W-orbit
33	[ 0, 0, 1, 0, 0, 0 ]	1	240
21	[ 0, 0, 0, 0, 1, 0 ]	2	60
1	[ 0, 0, 0, 0, 0, 0 ]	4	1

Highest weight: [ 0, 1, 0, 0, 0, 0 ]
Characteristic: 3
Dimension: 364

Level	dominant weight	weight multiplicity	length of W-orbit
36	[ 0, 1, 0, 0, 0, 0 ]	1	192
28	[ 0, 0, 0, 1, 0, 0 ]	1	160
12	[ 0, 0, 0, 0, 0, 1 ]	1	12

Highest weight: [ 1, 0, 0, 0, 0, 0 ]
Characteristic: 3
Dimension: 365

Level	dominant weight	weight multiplicity	length of W-orbit
37	[ 1, 0, 0, 0, 0, 0 ]	1	64
33	[ 0, 0, 1, 0, 0, 0 ]	1	240
21	[ 0, 0, 0, 0, 1, 0 ]	1	60
1	[ 0, 0, 0, 0, 0, 0 ]	1	1

Highest weight: [ 0, 0, 1, 0, 0, 0 ]
Characteristic: 5
Dimension: 428

Level	dominant weight	weight multiplicity	length of W-orbit
33	[ 0, 0, 1, 0, 0, 0 ]	1	240
21	[ 0, 0, 0, 0, 1, 0 ]	3	60
1	[ 0, 0, 0, 0, 0, 0 ]	8	1

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

Level	dominant weight	weight multiplicity	length of W-orbit
33	[ 0, 0, 1, 0, 0, 0 ]	1	240
21	[ 0, 0, 0, 0, 1, 0 ]	3	60
1	[ 0, 0, 0, 0, 0, 0 ]	9	1

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

Level	dominant weight	weight multiplicity	length of W-orbit
37	[ 1, 0, 0, 0, 0, 0 ]	1	64
33	[ 0, 0, 1, 0, 0, 0 ]	1	240
21	[ 0, 0, 0, 0, 1, 0 ]	2	60
1	[ 0, 0, 0, 0, 0, 0 ]	5	1

Highest weight: [ 0, 0, 0, 0, 1, 1 ]
Characteristic: 13
Dimension: 548

Level	dominant weight	weight multiplicity	length of W-orbit
32	[ 0, 0, 0, 0, 1, 1 ]	1	120
28	[ 0, 0, 0, 1, 0, 0 ]	2	160
12	[ 0, 0, 0, 0, 0, 1 ]	9	12

Highest weight: [ 0, 0, 0, 0, 1, 1 ]
Characteristic: not 3,13
Dimension: 560

Level	dominant weight	weight multiplicity	length of W-orbit
32	[ 0, 0, 0, 0, 1, 1 ]	1	120
28	[ 0, 0, 0, 1, 0, 0 ]	2	160
12	[ 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
36	[ 0, 1, 0, 0, 0, 0 ]	1	192
28	[ 0, 0, 0, 1, 0, 0 ]	2	160
12	[ 0, 0, 0, 0, 0, 1 ]	4	12

Highest weight: [ 0, 1, 0, 0, 0, 0 ]
Characteristic: not 2,3
Dimension: 572

Level	dominant weight	weight multiplicity	length of W-orbit
36	[ 0, 1, 0, 0, 0, 0 ]	1	192
28	[ 0, 0, 0, 1, 0, 0 ]	2	160
12	[ 0, 0, 0, 0, 0, 1 ]	5	12

Highest weight: [ 1, 0, 0, 0, 0, 1 ]
Characteristic: 2
Dimension: 768

Level	dominant weight	weight multiplicity	length of W-orbit
48	[ 1, 0, 0, 0, 0, 1 ]	1	384
36	[ 0, 1, 0, 0, 0, 0 ]	2	192

Highest weight: [ 0, 0, 0, 0, 2, 0 ]
Characteristic: 3
Dimension: 1221

Level	dominant weight	weight multiplicity	length of W-orbit
41	[ 0, 0, 0, 0, 2, 0 ]	1	60
39	[ 0, 0, 0, 1, 0, 1 ]	1	480
33	[ 0, 0, 1, 0, 0, 0 ]	1	240
23	[ 0, 0, 0, 0, 0, 2 ]	5	12
21	[ 0, 0, 0, 0, 1, 0 ]	6	60
1	[ 0, 0, 0, 0, 0, 0 ]	21	1

Highest weight: [ 0, 0, 0, 0, 0, 4 ]
Characteristic: not 2,3
Dimension: 1365

Level	dominant weight	weight multiplicity	length of W-orbit
45	[ 0, 0, 0, 0, 0, 4 ]	1	12
43	[ 0, 0, 0, 0, 1, 2 ]	1	120
41	[ 0, 0, 0, 0, 2, 0 ]	1	60
39	[ 0, 0, 0, 1, 0, 1 ]	1	480
33	[ 0, 0, 1, 0, 0, 0 ]	1	240
23	[ 0, 0, 0, 0, 0, 2 ]	6	12
21	[ 0, 0, 0, 0, 1, 0 ]	6	60
1	[ 0, 0, 0, 0, 0, 0 ]	21	1

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

Level	dominant weight	weight multiplicity	length of W-orbit
39	[ 0, 0, 0, 1, 0, 1 ]	1	480
33	[ 0, 0, 1, 0, 0, 0 ]	2	240
23	[ 0, 0, 0, 0, 0, 2 ]	4	12
21	[ 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: 7
Dimension: 1585

Level	dominant weight	weight multiplicity	length of W-orbit
41	[ 0, 0, 0, 0, 2, 0 ]	1	60
39	[ 0, 0, 0, 1, 0, 1 ]	1	480
33	[ 0, 0, 1, 0, 0, 0 ]	2	240
23	[ 0, 0, 0, 0, 0, 2 ]	5	12
21	[ 0, 0, 0, 0, 1, 0 ]	8	60
1	[ 0, 0, 0, 0, 0, 0 ]	25	1

Highest weight: [ 0, 0, 0, 0, 2, 0 ]
Characteristic: 13
Dimension: 1649

Level	dominant weight	weight multiplicity	length of W-orbit
41	[ 0, 0, 0, 0, 2, 0 ]	1	60
39	[ 0, 0, 0, 1, 0, 1 ]	1	480
33	[ 0, 0, 1, 0, 0, 0 ]	2	240
23	[ 0, 0, 0, 0, 0, 2 ]	5	12
21	[ 0, 0, 0, 0, 1, 0 ]	9	60
1	[ 0, 0, 0, 0, 0, 0 ]	29	1

Highest weight: [ 0, 0, 0, 0, 2, 0 ]
Characteristic: not 2,3,7,13
Dimension: 1650

Level	dominant weight	weight multiplicity	length of W-orbit
41	[ 0, 0, 0, 0, 2, 0 ]	1	60
39	[ 0, 0, 0, 1, 0, 1 ]	1	480
33	[ 0, 0, 1, 0, 0, 0 ]	2	240
23	[ 0, 0, 0, 0, 0, 2 ]	5	12
21	[ 0, 0, 0, 0, 1, 0 ]	9	60
1	[ 0, 0, 0, 0, 0, 0 ]	30	1

Highest weight: [ 0, 0, 0, 1, 0, 1 ]
Characteristic: 5
Dimension: 1924

Level	dominant weight	weight multiplicity	length of W-orbit
39	[ 0, 0, 0, 1, 0, 1 ]	1	480
33	[ 0, 0, 1, 0, 0, 0 ]	3	240
23	[ 0, 0, 0, 0, 0, 2 ]	3	12
21	[ 0, 0, 0, 0, 1, 0 ]	11	60
1	[ 0, 0, 0, 0, 0, 0 ]	28	1

Highest weight: [ 0, 0, 0, 1, 0, 1 ]
Characteristic: 3
Dimension: 1938

Level	dominant weight	weight multiplicity	length of W-orbit
39	[ 0, 0, 0, 1, 0, 1 ]	1	480
33	[ 0, 0, 1, 0, 0, 0 ]	3	240
23	[ 0, 0, 0, 0, 0, 2 ]	4	12
21	[ 0, 0, 0, 0, 1, 0 ]	11	60
1	[ 0, 0, 0, 0, 0, 0 ]	30	1

Highest weight: [ 0, 0, 0, 1, 0, 1 ]
Characteristic: not 2,3,5
Dimension: 2002

Level	dominant weight	weight multiplicity	length of W-orbit
39	[ 0, 0, 0, 1, 0, 1 ]	1	480
33	[ 0, 0, 1, 0, 0, 0 ]	3	240
23	[ 0, 0, 0, 0, 0, 2 ]	4	12
21	[ 0, 0, 0, 0, 1, 0 ]	12	60
1	[ 0, 0, 0, 0, 0, 0 ]	34	1

Highest weight: [ 0, 0, 0, 0, 1, 2 ]
Characteristic: 7
Dimension: 2847

Level	dominant weight	weight multiplicity	length of W-orbit
43	[ 0, 0, 0, 0, 1, 2 ]	1	120
41	[ 0, 0, 0, 0, 2, 0 ]	1	60
39	[ 0, 0, 0, 1, 0, 1 ]	2	480
33	[ 0, 0, 1, 0, 0, 0 ]	3	240
23	[ 0, 0, 0, 0, 0, 2 ]	9	12
21	[ 0, 0, 0, 0, 1, 0 ]	14	60
1	[ 0, 0, 0, 0, 0, 0 ]	39	1

Highest weight: [ 0, 0, 0, 0, 1, 2 ]
Characteristic: not 2,7
Dimension: 2925

Level	dominant weight	weight multiplicity	length of W-orbit
43	[ 0, 0, 0, 0, 1, 2 ]	1	120
41	[ 0, 0, 0, 0, 2, 0 ]	1	60
39	[ 0, 0, 0, 1, 0, 1 ]	2	480
33	[ 0, 0, 1, 0, 0, 0 ]	3	240
23	[ 0, 0, 0, 0, 0, 2 ]	10	12
21	[ 0, 0, 0, 0, 1, 0 ]	15	60
1	[ 0, 0, 0, 0, 0, 0 ]	45	1

Highest weight: [ 0, 0, 0, 1, 1, 0 ]
Characteristic: 3
Dimension: 3432

Level	dominant weight	weight multiplicity	length of W-orbit
48	[ 0, 0, 0, 1, 1, 0 ]	1	480
44	[ 0, 0, 1, 0, 0, 1 ]	1	960
36	[ 0, 1, 0, 0, 0, 0 ]	1	192
32	[ 0, 0, 0, 0, 1, 1 ]	5	120
28	[ 0, 0, 0, 1, 0, 0 ]	6	160
12	[ 0, 0, 0, 0, 0, 1 ]	20	12

Highest weight: [ 0, 1, 0, 0, 0, 1 ]
Characteristic: 3
Dimension: 3638

Level	dominant weight	weight multiplicity	length of W-orbit
47	[ 0, 1, 0, 0, 0, 1 ]	1	960
39	[ 0, 0, 0, 1, 0, 1 ]	1	480
37	[ 1, 0, 0, 0, 0, 0 ]	4	64
33	[ 0, 0, 1, 0, 0, 0 ]	6	240
23	[ 0, 0, 0, 0, 0, 2 ]	1	12
21	[ 0, 0, 0, 0, 1, 0 ]	8	60
1	[ 0, 0, 0, 0, 0, 0 ]	10	1

Highest weight: [ 1, 0, 0, 0, 0, 1 ]
Characteristic: 3
Dimension: 3652

Level	dominant weight	weight multiplicity	length of W-orbit
48	[ 1, 0, 0, 0, 0, 1 ]	1	384
44	[ 0, 0, 1, 0, 0, 1 ]	1	960
36	[ 0, 1, 0, 0, 0, 0 ]	5	192
32	[ 0, 0, 0, 0, 1, 1 ]	1	120
28	[ 0, 0, 0, 1, 0, 0 ]	7	160
12	[ 0, 0, 0, 0, 0, 1 ]	9	12

Highest weight: [ 0, 0, 1, 0, 0, 1 ]
Characteristic: 5
Dimension: 3796

Level	dominant weight	weight multiplicity	length of W-orbit
44	[ 0, 0, 1, 0, 0, 1 ]	1	960
36	[ 0, 1, 0, 0, 0, 0 ]	3	192
32	[ 0, 0, 0, 0, 1, 1 ]	3	120
28	[ 0, 0, 0, 1, 0, 0 ]	10	160
12	[ 0, 0, 0, 0, 0, 1 ]	25	12

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

Level	dominant weight	weight multiplicity	length of W-orbit
44	[ 0, 0, 1, 0, 0, 1 ]	1	960
36	[ 0, 1, 0, 0, 0, 0 ]	4	192
32	[ 0, 0, 0, 0, 1, 1 ]	2	120
28	[ 0, 0, 0, 1, 0, 0 ]	10	160
12	[ 0, 0, 0, 0, 0, 1 ]	20	12