Weight Multiplicities

Groups of type F4, degree bound 12000

Diagram:

1 - 2 > 3 - 4

Overview

Dimension	Highest weight	Characteristic
1	[ 0, 0, 0, 0 ]	all
25	[ 0, 0, 0, 1 ]	3
26	[ 0, 0, 0, 1 ]	not 3
26	[ 1, 0, 0, 0 ]	2
52	[ 1, 0, 0, 0 ]	not 2
196	[ 0, 0, 1, 0 ]	3
246	[ 0, 0, 1, 0 ]	2
246	[ 0, 1, 0, 0 ]	2
273	[ 0, 0, 1, 0 ]	not 2, 3
298	[ 0, 0, 0, 2 ]	7
323	[ 0, 0, 0, 2 ]	13
324	[ 0, 0, 0, 2 ]	not 2, 7, 13
676	[ 1, 0, 0, 1 ]	2
755	[ 2, 0, 0, 0 ]	7
1053	[ 1, 0, 0, 1 ]	not 2
1053	[ 2, 0, 0, 0 ]	not 2, 7
1222	[ 0, 1, 0, 0 ]	3
1274	[ 0, 1, 0, 0 ]	not 2, 3
2404	[ 0, 0, 1, 1 ]	3
2651	[ 0, 0, 0, 3 ]	7
2652	[ 0, 0, 0, 3 ]	not 2, 3, 7
2991	[ 0, 0, 1, 1 ]	7
3773	[ 0, 0, 1, 1 ]	13
4096	[ 0, 0, 1, 1 ]	not 3, 7, 13
4096	[ 1, 1, 0, 0 ]	2
4380	[ 1, 0, 1, 0 ]	7
5369	[ 1, 1, 0, 0 ]	3
6396	[ 0, 1, 0, 1 ]	2
6396	[ 1, 0, 1, 0 ]	2
6707	[ 1, 0, 0, 2 ]	3
7371	[ 1, 0, 1, 0 ]	3
8424	[ 1, 0, 1, 0 ]	not 2, 3, 7
9477	[ 2, 0, 0, 1 ]	5
10829	[ 1, 0, 0, 2 ]	not 2, 3
11102	[ 3, 0, 0, 0 ]	5
11739	[ 0, 1, 1, 0 ]	5
11907	[ 0, 1, 0, 1 ]	3

The characters

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

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

Highest weight: [ 0, 0, 0, 1 ]
Characteristic: 3
Dimension: 25

Level	dominant weight	weight multiplicity	length of W-orbit
17	[ 0, 0, 0, 1 ]	1	24
1	[ 0, 0, 0, 0 ]	1	1

Highest weight: [ 0, 0, 0, 1 ]
Characteristic: not 3
Dimension: 26

Level	dominant weight	weight multiplicity	length of W-orbit
17	[ 0, 0, 0, 1 ]	1	24
1	[ 0, 0, 0, 0 ]	2	1

Highest weight: [ 1, 0, 0, 0 ]
Characteristic: 2
Dimension: 26

Level	dominant weight	weight multiplicity	length of W-orbit
23	[ 1, 0, 0, 0 ]	1	24
1	[ 0, 0, 0, 0 ]	2	1

Highest weight: [ 1, 0, 0, 0 ]
Characteristic: not 2
Dimension: 52

Level	dominant weight	weight multiplicity	length of W-orbit
23	[ 1, 0, 0, 0 ]	1	24
17	[ 0, 0, 0, 1 ]	1	24
1	[ 0, 0, 0, 0 ]	4	1

Highest weight: [ 0, 0, 1, 0 ]
Characteristic: 3
Dimension: 196

Level	dominant weight	weight multiplicity	length of W-orbit
31	[ 0, 0, 1, 0 ]	1	96
23	[ 1, 0, 0, 0 ]	1	24
17	[ 0, 0, 0, 1 ]	3	24
1	[ 0, 0, 0, 0 ]	4	1

Highest weight: [ 0, 0, 1, 0 ]
Characteristic: 2
Dimension: 246

Level	dominant weight	weight multiplicity	length of W-orbit
31	[ 0, 0, 1, 0 ]	1	96
23	[ 1, 0, 0, 0 ]	2	24
17	[ 0, 0, 0, 1 ]	4	24
1	[ 0, 0, 0, 0 ]	6	1

Highest weight: [ 0, 1, 0, 0 ]
Characteristic: 2
Dimension: 246

Level	dominant weight	weight multiplicity	length of W-orbit
43	[ 0, 1, 0, 0 ]	1	96
33	[ 0, 0, 0, 2 ]	2	24
23	[ 1, 0, 0, 0 ]	4	24
1	[ 0, 0, 0, 0 ]	6	1

Highest weight: [ 0, 0, 1, 0 ]
Characteristic: not 2,3
Dimension: 273

Level	dominant weight	weight multiplicity	length of W-orbit
31	[ 0, 0, 1, 0 ]	1	96
23	[ 1, 0, 0, 0 ]	2	24
17	[ 0, 0, 0, 1 ]	5	24
1	[ 0, 0, 0, 0 ]	9	1

Highest weight: [ 0, 0, 0, 2 ]
Characteristic: 7
Dimension: 298

Level	dominant weight	weight multiplicity	length of W-orbit
33	[ 0, 0, 0, 2 ]	1	24
31	[ 0, 0, 1, 0 ]	1	96
23	[ 1, 0, 0, 0 ]	3	24
17	[ 0, 0, 0, 1 ]	4	24
1	[ 0, 0, 0, 0 ]	10	1

Highest weight: [ 0, 0, 0, 2 ]
Characteristic: 13
Dimension: 323

Level	dominant weight	weight multiplicity	length of W-orbit
33	[ 0, 0, 0, 2 ]	1	24
31	[ 0, 0, 1, 0 ]	1	96
23	[ 1, 0, 0, 0 ]	3	24
17	[ 0, 0, 0, 1 ]	5	24
1	[ 0, 0, 0, 0 ]	11	1

Highest weight: [ 0, 0, 0, 2 ]
Characteristic: not 2,7,13
Dimension: 324

Level	dominant weight	weight multiplicity	length of W-orbit
33	[ 0, 0, 0, 2 ]	1	24
31	[ 0, 0, 1, 0 ]	1	96
23	[ 1, 0, 0, 0 ]	3	24
17	[ 0, 0, 0, 1 ]	5	24
1	[ 0, 0, 0, 0 ]	12	1

Highest weight: [ 1, 0, 0, 1 ]
Characteristic: 2
Dimension: 676

Level	dominant weight	weight multiplicity	length of W-orbit
39	[ 1, 0, 0, 1 ]	1	144
31	[ 0, 0, 1, 0 ]	3	96
23	[ 1, 0, 0, 0 ]	2	24
17	[ 0, 0, 0, 1 ]	8	24
1	[ 0, 0, 0, 0 ]	4	1

Highest weight: [ 2, 0, 0, 0 ]
Characteristic: 7
Dimension: 755

Level	dominant weight	weight multiplicity	length of W-orbit
45	[ 2, 0, 0, 0 ]	1	24
43	[ 0, 1, 0, 0 ]	1	96
39	[ 1, 0, 0, 1 ]	1	144
33	[ 0, 0, 0, 2 ]	2	24
31	[ 0, 0, 1, 0 ]	2	96
23	[ 1, 0, 0, 0 ]	5	24
17	[ 0, 0, 0, 1 ]	5	24
1	[ 0, 0, 0, 0 ]	11	1

Highest weight: [ 1, 0, 0, 1 ]
Characteristic: not 2
Dimension: 1053

Level	dominant weight	weight multiplicity	length of W-orbit
39	[ 1, 0, 0, 1 ]	1	144
33	[ 0, 0, 0, 2 ]	1	24
31	[ 0, 0, 1, 0 ]	4	96
23	[ 1, 0, 0, 0 ]	6	24
17	[ 0, 0, 0, 1 ]	14	24
1	[ 0, 0, 0, 0 ]	21	1

Highest weight: [ 2, 0, 0, 0 ]
Characteristic: not 2,7
Dimension: 1053

Level	dominant weight	weight multiplicity	length of W-orbit
45	[ 2, 0, 0, 0 ]	1	24
43	[ 0, 1, 0, 0 ]	1	96
39	[ 1, 0, 0, 1 ]	1	144
33	[ 0, 0, 0, 2 ]	3	24
31	[ 0, 0, 1, 0 ]	3	96
23	[ 1, 0, 0, 0 ]	8	24
17	[ 0, 0, 0, 1 ]	9	24
1	[ 0, 0, 0, 0 ]	21	1

Highest weight: [ 0, 1, 0, 0 ]
Characteristic: 3
Dimension: 1222

Level	dominant weight	weight multiplicity	length of W-orbit
43	[ 0, 1, 0, 0 ]	1	96
39	[ 1, 0, 0, 1 ]	1	144
33	[ 0, 0, 0, 2 ]	3	24
31	[ 0, 0, 1, 0 ]	4	96
23	[ 1, 0, 0, 0 ]	9	24
17	[ 0, 0, 0, 1 ]	12	24
1	[ 0, 0, 0, 0 ]	22	1

Highest weight: [ 0, 1, 0, 0 ]
Characteristic: not 2,3
Dimension: 1274

Level	dominant weight	weight multiplicity	length of W-orbit
43	[ 0, 1, 0, 0 ]	1	96
39	[ 1, 0, 0, 1 ]	1	144
33	[ 0, 0, 0, 2 ]	3	24
31	[ 0, 0, 1, 0 ]	4	96
23	[ 1, 0, 0, 0 ]	10	24
17	[ 0, 0, 0, 1 ]	13	24
1	[ 0, 0, 0, 0 ]	26	1

Highest weight: [ 0, 0, 1, 1 ]
Characteristic: 3
Dimension: 2404

Level	dominant weight	weight multiplicity	length of W-orbit
47	[ 0, 0, 1, 1 ]	1	192
43	[ 0, 1, 0, 0 ]	1	96
39	[ 1, 0, 0, 1 ]	3	144
33	[ 0, 0, 0, 2 ]	5	24
31	[ 0, 0, 1, 0 ]	8	96
23	[ 1, 0, 0, 0 ]	12	24
17	[ 0, 0, 0, 1 ]	20	24
1	[ 0, 0, 0, 0 ]	28	1

Highest weight: [ 0, 0, 0, 3 ]
Characteristic: 7
Dimension: 2651

Level	dominant weight	weight multiplicity	length of W-orbit
49	[ 0, 0, 0, 3 ]	1	24
47	[ 0, 0, 1, 1 ]	1	192
43	[ 0, 1, 0, 0 ]	1	96
39	[ 1, 0, 0, 1 ]	3	144
33	[ 0, 0, 0, 2 ]	5	24
31	[ 0, 0, 1, 0 ]	9	96
23	[ 1, 0, 0, 0 ]	13	24
17	[ 0, 0, 0, 1 ]	24	24
1	[ 0, 0, 0, 0 ]	35	1

Highest weight: [ 0, 0, 0, 3 ]
Characteristic: not 2,3,7
Dimension: 2652

Level	dominant weight	weight multiplicity	length of W-orbit
49	[ 0, 0, 0, 3 ]	1	24
47	[ 0, 0, 1, 1 ]	1	192
43	[ 0, 1, 0, 0 ]	1	96
39	[ 1, 0, 0, 1 ]	3	144
33	[ 0, 0, 0, 2 ]	5	24
31	[ 0, 0, 1, 0 ]	9	96
23	[ 1, 0, 0, 0 ]	13	24
17	[ 0, 0, 0, 1 ]	24	24
1	[ 0, 0, 0, 0 ]	36	1

Highest weight: [ 0, 0, 1, 1 ]
Characteristic: 7
Dimension: 2991

Level	dominant weight	weight multiplicity	length of W-orbit
47	[ 0, 0, 1, 1 ]	1	192
43	[ 0, 1, 0, 0 ]	2	96
39	[ 1, 0, 0, 1 ]	3	144
33	[ 0, 0, 0, 2 ]	7	24
31	[ 0, 0, 1, 0 ]	10	96
23	[ 1, 0, 0, 0 ]	17	24
17	[ 0, 0, 0, 1 ]	25	24
1	[ 0, 0, 0, 0 ]	39	1

Highest weight: [ 0, 0, 1, 1 ]
Characteristic: 13
Dimension: 3773

Level	dominant weight	weight multiplicity	length of W-orbit
47	[ 0, 0, 1, 1 ]	1	192
43	[ 0, 1, 0, 0 ]	2	96
39	[ 1, 0, 0, 1 ]	4	144
33	[ 0, 0, 0, 2 ]	7	24
31	[ 0, 0, 1, 0 ]	13	96
23	[ 1, 0, 0, 0 ]	21	24
17	[ 0, 0, 0, 1 ]	35	24
1	[ 0, 0, 0, 0 ]	53	1

Highest weight: [ 0, 0, 1, 1 ]
Characteristic: not 3,7,13
Dimension: 4096

Level	dominant weight	weight multiplicity	length of W-orbit
47	[ 0, 0, 1, 1 ]	1	192
43	[ 0, 1, 0, 0 ]	2	96
39	[ 1, 0, 0, 1 ]	4	144
33	[ 0, 0, 0, 2 ]	8	24
31	[ 0, 0, 1, 0 ]	14	96
23	[ 1, 0, 0, 0 ]	24	24
17	[ 0, 0, 0, 1 ]	40	24
1	[ 0, 0, 0, 0 ]	64	1

Highest weight: [ 1, 1, 0, 0 ]
Characteristic: 2
Dimension: 4096

Level	dominant weight	weight multiplicity	length of W-orbit
65	[ 1, 1, 0, 0 ]	1	192
61	[ 0, 0, 2, 0 ]	2	96
55	[ 1, 0, 0, 2 ]	4	144
45	[ 2, 0, 0, 0 ]	8	24
43	[ 0, 1, 0, 0 ]	14	96
33	[ 0, 0, 0, 2 ]	24	24
23	[ 1, 0, 0, 0 ]	40	24
1	[ 0, 0, 0, 0 ]	64	1

Highest weight: [ 1, 0, 1, 0 ]
Characteristic: 7
Dimension: 4380

Level	dominant weight	weight multiplicity	length of W-orbit
53	[ 1, 0, 1, 0 ]	1	288
47	[ 0, 0, 1, 1 ]	2	192
45	[ 2, 0, 0, 0 ]	2	24
43	[ 0, 1, 0, 0 ]	3	96
39	[ 1, 0, 0, 1 ]	6	144
33	[ 0, 0, 0, 2 ]	7	24
31	[ 0, 0, 1, 0 ]	13	96
23	[ 1, 0, 0, 0 ]	17	24
17	[ 0, 0, 0, 1 ]	27	24
1	[ 0, 0, 0, 0 ]	36	1

Highest weight: [ 1, 1, 0, 0 ]
Characteristic: 3
Dimension: 5369

Level	dominant weight	weight multiplicity	length of W-orbit
65	[ 1, 1, 0, 0 ]	1	192
61	[ 2, 0, 0, 1 ]	1	144
61	[ 0, 0, 2, 0 ]	1	96
59	[ 0, 1, 0, 1 ]	1	288
55	[ 1, 0, 0, 2 ]	2	144
53	[ 1, 0, 1, 0 ]	2	288
49	[ 0, 0, 0, 3 ]	1	24
47	[ 0, 0, 1, 1 ]	3	192
45	[ 2, 0, 0, 0 ]	5	24
43	[ 0, 1, 0, 0 ]	6	96
39	[ 1, 0, 0, 1 ]	6	144
33	[ 0, 0, 0, 2 ]	9	24
31	[ 0, 0, 1, 0 ]	8	96
23	[ 1, 0, 0, 0 ]	14	24
17	[ 0, 0, 0, 1 ]	12	24
1	[ 0, 0, 0, 0 ]	17	1

Highest weight: [ 0, 1, 0, 1 ]
Characteristic: 2
Dimension: 6396

Level	dominant weight	weight multiplicity	length of W-orbit
59	[ 0, 1, 0, 1 ]	1	288
53	[ 1, 0, 1, 0 ]	2	288
49	[ 0, 0, 0, 3 ]	2	24
47	[ 0, 0, 1, 1 ]	5	192
43	[ 0, 1, 0, 0 ]	2	96
39	[ 1, 0, 0, 1 ]	10	144
33	[ 0, 0, 0, 2 ]	4	24
31	[ 0, 0, 1, 0 ]	19	96
23	[ 1, 0, 0, 0 ]	8	24
17	[ 0, 0, 0, 1 ]	32	24
1	[ 0, 0, 0, 0 ]	12	1

Highest weight: [ 1, 0, 1, 0 ]
Characteristic: 2
Dimension: 6396

Level	dominant weight	weight multiplicity	length of W-orbit
53	[ 1, 0, 1, 0 ]	1	288
47	[ 0, 0, 1, 1 ]	3	192
45	[ 2, 0, 0, 0 ]	2	24
43	[ 0, 1, 0, 0 ]	4	96
39	[ 1, 0, 0, 1 ]	8	144
33	[ 0, 0, 0, 2 ]	12	24
31	[ 0, 0, 1, 0 ]	20	96
23	[ 1, 0, 0, 0 ]	26	24
17	[ 0, 0, 0, 1 ]	44	24
1	[ 0, 0, 0, 0 ]	60	1

Highest weight: [ 1, 0, 0, 2 ]
Characteristic: 3
Dimension: 6707

Level	dominant weight	weight multiplicity	length of W-orbit
55	[ 1, 0, 0, 2 ]	1	144
53	[ 1, 0, 1, 0 ]	1	288
49	[ 0, 0, 0, 3 ]	1	24
47	[ 0, 0, 1, 1 ]	3	192
45	[ 2, 0, 0, 0 ]	3	24
43	[ 0, 1, 0, 0 ]	7	96
39	[ 1, 0, 0, 1 ]	8	144
33	[ 0, 0, 0, 2 ]	15	24
31	[ 0, 0, 1, 0 ]	18	96
23	[ 1, 0, 0, 0 ]	31	24
17	[ 0, 0, 0, 1 ]	37	24
1	[ 0, 0, 0, 0 ]	59	1

Highest weight: [ 1, 0, 1, 0 ]
Characteristic: 3
Dimension: 7371

Level	dominant weight	weight multiplicity	length of W-orbit
53	[ 1, 0, 1, 0 ]	1	288
47	[ 0, 0, 1, 1 ]	3	192
45	[ 2, 0, 0, 0 ]	1	24
43	[ 0, 1, 0, 0 ]	4	96
39	[ 1, 0, 0, 1 ]	9	144
33	[ 0, 0, 0, 2 ]	12	24
31	[ 0, 0, 1, 0 ]	24	96
23	[ 1, 0, 0, 0 ]	32	24
17	[ 0, 0, 0, 1 ]	57	24
1	[ 0, 0, 0, 0 ]	75	1

Highest weight: [ 1, 0, 1, 0 ]
Characteristic: not 2,3,7
Dimension: 8424

Level	dominant weight	weight multiplicity	length of W-orbit
53	[ 1, 0, 1, 0 ]	1	288
47	[ 0, 0, 1, 1 ]	3	192
45	[ 2, 0, 0, 0 ]	2	24
43	[ 0, 1, 0, 0 ]	5	96
39	[ 1, 0, 0, 1 ]	10	144
33	[ 0, 0, 0, 2 ]	15	24
31	[ 0, 0, 1, 0 ]	27	96
23	[ 1, 0, 0, 0 ]	40	24
17	[ 0, 0, 0, 1 ]	66	24
1	[ 0, 0, 0, 0 ]	96	1

Highest weight: [ 2, 0, 0, 1 ]
Characteristic: 5
Dimension: 9477

Level	dominant weight	weight multiplicity	length of W-orbit
61	[ 2, 0, 0, 1 ]	1	144
59	[ 0, 1, 0, 1 ]	1	288
55	[ 1, 0, 0, 2 ]	1	144
53	[ 1, 0, 1, 0 ]	3	288
49	[ 0, 0, 0, 3 ]	3	24
47	[ 0, 0, 1, 1 ]	6	192
45	[ 2, 0, 0, 0 ]	4	24
43	[ 0, 1, 0, 0 ]	7	96
39	[ 1, 0, 0, 1 ]	13	144
33	[ 0, 0, 0, 2 ]	14	24
31	[ 0, 0, 1, 0 ]	23	96
23	[ 1, 0, 0, 0 ]	26	24
17	[ 0, 0, 0, 1 ]	40	24
1	[ 0, 0, 0, 0 ]	45	1

Highest weight: [ 1, 0, 0, 2 ]
Characteristic: not 2,3
Dimension: 10829

Level	dominant weight	weight multiplicity	length of W-orbit
55	[ 1, 0, 0, 2 ]	1	144
53	[ 1, 0, 1, 0 ]	1	288
49	[ 0, 0, 0, 3 ]	1	24
47	[ 0, 0, 1, 1 ]	4	192
45	[ 2, 0, 0, 0 ]	3	24
43	[ 0, 1, 0, 0 ]	9	96
39	[ 1, 0, 0, 1 ]	12	144
33	[ 0, 0, 0, 2 ]	23	24
31	[ 0, 0, 1, 0 ]	32	96
23	[ 1, 0, 0, 0 ]	56	24
17	[ 0, 0, 0, 1 ]	77	24
1	[ 0, 0, 0, 0 ]	125	1

Highest weight: [ 3, 0, 0, 0 ]
Characteristic: 5
Dimension: 11102

Level	dominant weight	weight multiplicity	length of W-orbit
67	[ 3, 0, 0, 0 ]	1	24
65	[ 1, 1, 0, 0 ]	1	192
61	[ 2, 0, 0, 1 ]	1	144
61	[ 0, 0, 2, 0 ]	1	96
59	[ 0, 1, 0, 1 ]	1	288
55	[ 1, 0, 0, 2 ]	3	144
53	[ 1, 0, 1, 0 ]	3	288
49	[ 0, 0, 0, 3 ]	3	24
47	[ 0, 0, 1, 1 ]	6	192
45	[ 2, 0, 0, 0 ]	8	24
43	[ 0, 1, 0, 0 ]	12	96
39	[ 1, 0, 0, 1 ]	13	144
33	[ 0, 0, 0, 2 ]	21	24
31	[ 0, 0, 1, 0 ]	23	96
23	[ 1, 0, 0, 0 ]	37	24
17	[ 0, 0, 0, 1 ]	40	24
1	[ 0, 0, 0, 0 ]	62	1

Highest weight: [ 0, 1, 1, 0 ]
Characteristic: 5
Dimension: 11739

Level	dominant weight	weight multiplicity	length of W-orbit
73	[ 0, 1, 1, 0 ]	1	288
69	[ 1, 0, 1, 1 ]	1	576
65	[ 1, 1, 0, 0 ]	1	192
63	[ 0, 0, 1, 2 ]	2	192
61	[ 2, 0, 0, 1 ]	1	144
61	[ 0, 0, 2, 0 ]	2	96
59	[ 0, 1, 0, 1 ]	3	288
55	[ 1, 0, 0, 2 ]	3	144
53	[ 1, 0, 1, 0 ]	5	288
49	[ 0, 0, 0, 3 ]	5	24
47	[ 0, 0, 1, 1 ]	8	192
45	[ 2, 0, 0, 0 ]	5	24
43	[ 0, 1, 0, 0 ]	8	96
39	[ 1, 0, 0, 1 ]	12	144
33	[ 0, 0, 0, 2 ]	12	24
31	[ 0, 0, 1, 0 ]	17	96
23	[ 1, 0, 0, 0 ]	18	24
17	[ 0, 0, 0, 1 ]	24	24
1	[ 0, 0, 0, 0 ]	27	1

Highest weight: [ 0, 1, 0, 1 ]
Characteristic: 3
Dimension: 11907

Level	dominant weight	weight multiplicity	length of W-orbit
59	[ 0, 1, 0, 1 ]	1	288
55	[ 1, 0, 0, 2 ]	1	144
53	[ 1, 0, 1, 0 ]	2	288
49	[ 0, 0, 0, 3 ]	3	24
47	[ 0, 0, 1, 1 ]	6	192
45	[ 2, 0, 0, 0 ]	3	24
43	[ 0, 1, 0, 0 ]	9	96
39	[ 1, 0, 0, 1 ]	15	144
33	[ 0, 0, 0, 2 ]	21	24
31	[ 0, 0, 1, 0 ]	33	96
23	[ 1, 0, 0, 0 ]	48	24
17	[ 0, 0, 0, 1 ]	69	24
1	[ 0, 0, 0, 0 ]	99	1