Weight Multiplicities

Groups of type D7, degree bound 5000

Diagram:

 1
  \
   3 - 4 - .. - 7
  /
 2

Overview

Dimension	Highest weight	Characteristic
1	[ 0, 0, 0, 0, 0, 0, 0 ]	all
14	[ 0, 0, 0, 0, 0, 0, 1 ]	all
64	[ 0, 1, 0, 0, 0, 0, 0 ]	all
64	[ 1, 0, 0, 0, 0, 0, 0 ]	all
90	[ 0, 0, 0, 0, 0, 1, 0 ]	2
91	[ 0, 0, 0, 0, 0, 1, 0 ]	not 2
103	[ 0, 0, 0, 0, 0, 0, 2 ]	7
104	[ 0, 0, 0, 0, 0, 0, 2 ]	not 2, 7
336	[ 0, 0, 0, 0, 1, 0, 0 ]	2
364	[ 0, 0, 0, 0, 1, 0, 0 ]	not 2
532	[ 0, 0, 0, 0, 0, 1, 1 ]	3
546	[ 0, 0, 0, 0, 0, 0, 3 ]	not 2, 3
768	[ 0, 1, 0, 0, 0, 0, 1 ]	7
768	[ 1, 0, 0, 0, 0, 0, 1 ]	7
832	[ 0, 1, 0, 0, 0, 0, 1 ]	not 7
832	[ 1, 0, 0, 0, 0, 0, 1 ]	not 7
882	[ 0, 0, 0, 0, 0, 1, 1 ]	13
896	[ 0, 0, 0, 0, 0, 1, 1 ]	not 3, 13
910	[ 0, 0, 0, 1, 0, 0, 0 ]	2
1001	[ 0, 0, 0, 1, 0, 0, 0 ]	not 2
1288	[ 0, 0, 1, 0, 0, 0, 0 ]	2
1716	[ 0, 2, 0, 0, 0, 0, 0 ]	not 2
1716	[ 2, 0, 0, 0, 0, 0, 0 ]	not 2
1912	[ 1, 1, 0, 0, 0, 0, 0 ]	2
1975	[ 0, 0, 0, 0, 0, 2, 0 ]	3
2002	[ 0, 0, 1, 0, 0, 0, 0 ]	not 2
2275	[ 0, 0, 0, 0, 0, 0, 4 ]	not 2, 3
2884	[ 0, 0, 0, 0, 1, 0, 1 ]	2
3003	[ 1, 1, 0, 0, 0, 0, 0 ]	not 2
3079	[ 0, 0, 0, 0, 0, 2, 0 ]	13
3080	[ 0, 0, 0, 0, 0, 2, 0 ]	not 2, 3, 13
3913	[ 0, 0, 0, 0, 1, 0, 1 ]	3
4004	[ 0, 0, 0, 0, 1, 0, 1 ]	not 2, 3
4096	[ 0, 1, 0, 0, 0, 1, 0 ]	2
4096	[ 0, 1, 0, 0, 0, 1, 0 ]	3
4096	[ 1, 0, 0, 0, 0, 1, 0 ]	2
4096	[ 1, 0, 0, 0, 0, 1, 0 ]	3
4864	[ 0, 1, 0, 0, 0, 1, 0 ]	13
4864	[ 1, 0, 0, 0, 0, 1, 0 ]	13
4928	[ 0, 1, 0, 0, 0, 1, 0 ]	not 2, 3, 13
4928	[ 1, 0, 0, 0, 0, 1, 0 ]	not 2, 3, 13

The characters

Highest weight: [ 0, 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, 0 ]	1	1

Highest weight: [ 0, 0, 0, 0, 0, 0, 1 ]
Characteristic: all
Dimension: 14

Level	dominant weight	weight multiplicity	length of W-orbit
13	[ 0, 0, 0, 0, 0, 0, 1 ]	1	14

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

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

Highest weight: [ 1, 0, 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, 0 ]	1	64

Highest weight: [ 0, 0, 0, 0, 0, 1, 0 ]
Characteristic: 2
Dimension: 90

Level	dominant weight	weight multiplicity	length of W-orbit
23	[ 0, 0, 0, 0, 0, 1, 0 ]	1	84
1	[ 0, 0, 0, 0, 0, 0, 0 ]	6	1

Highest weight: [ 0, 0, 0, 0, 0, 1, 0 ]
Characteristic: not 2
Dimension: 91

Level	dominant weight	weight multiplicity	length of W-orbit
23	[ 0, 0, 0, 0, 0, 1, 0 ]	1	84
1	[ 0, 0, 0, 0, 0, 0, 0 ]	7	1

Highest weight: [ 0, 0, 0, 0, 0, 0, 2 ]
Characteristic: 7
Dimension: 103

Level	dominant weight	weight multiplicity	length of W-orbit
25	[ 0, 0, 0, 0, 0, 0, 2 ]	1	14
23	[ 0, 0, 0, 0, 0, 1, 0 ]	1	84
1	[ 0, 0, 0, 0, 0, 0, 0 ]	5	1

Highest weight: [ 0, 0, 0, 0, 0, 0, 2 ]
Characteristic: not 2,7
Dimension: 104

Level	dominant weight	weight multiplicity	length of W-orbit
25	[ 0, 0, 0, 0, 0, 0, 2 ]	1	14
23	[ 0, 0, 0, 0, 0, 1, 0 ]	1	84
1	[ 0, 0, 0, 0, 0, 0, 0 ]	6	1

Highest weight: [ 0, 0, 0, 0, 1, 0, 0 ]
Characteristic: 2
Dimension: 336

Level	dominant weight	weight multiplicity	length of W-orbit
31	[ 0, 0, 0, 0, 1, 0, 0 ]	1	280
13	[ 0, 0, 0, 0, 0, 0, 1 ]	4	14

Highest weight: [ 0, 0, 0, 0, 1, 0, 0 ]
Characteristic: not 2
Dimension: 364

Level	dominant weight	weight multiplicity	length of W-orbit
31	[ 0, 0, 0, 0, 1, 0, 0 ]	1	280
13	[ 0, 0, 0, 0, 0, 0, 1 ]	6	14

Highest weight: [ 0, 0, 0, 0, 0, 1, 1 ]
Characteristic: 3
Dimension: 532

Level	dominant weight	weight multiplicity	length of W-orbit
35	[ 0, 0, 0, 0, 0, 1, 1 ]	1	168
31	[ 0, 0, 0, 0, 1, 0, 0 ]	1	280
13	[ 0, 0, 0, 0, 0, 0, 1 ]	6	14

Highest weight: [ 0, 0, 0, 0, 0, 0, 3 ]
Characteristic: not 2,3
Dimension: 546

Level	dominant weight	weight multiplicity	length of W-orbit
37	[ 0, 0, 0, 0, 0, 0, 3 ]	1	14
35	[ 0, 0, 0, 0, 0, 1, 1 ]	1	168
31	[ 0, 0, 0, 0, 1, 0, 0 ]	1	280
13	[ 0, 0, 0, 0, 0, 0, 1 ]	6	14

Highest weight: [ 0, 1, 0, 0, 0, 0, 1 ]
Characteristic: 7
Dimension: 768

Level	dominant weight	weight multiplicity	length of W-orbit
34	[ 0, 1, 0, 0, 0, 0, 1 ]	1	448
22	[ 1, 0, 0, 0, 0, 0, 0 ]	5	64

Highest weight: [ 1, 0, 0, 0, 0, 0, 1 ]
Characteristic: 7
Dimension: 768

Level	dominant weight	weight multiplicity	length of W-orbit
34	[ 1, 0, 0, 0, 0, 0, 1 ]	1	448
22	[ 0, 1, 0, 0, 0, 0, 0 ]	5	64

Highest weight: [ 0, 1, 0, 0, 0, 0, 1 ]
Characteristic: not 7
Dimension: 832

Level	dominant weight	weight multiplicity	length of W-orbit
34	[ 0, 1, 0, 0, 0, 0, 1 ]	1	448
22	[ 1, 0, 0, 0, 0, 0, 0 ]	6	64

Highest weight: [ 1, 0, 0, 0, 0, 0, 1 ]
Characteristic: not 7
Dimension: 832

Level	dominant weight	weight multiplicity	length of W-orbit
34	[ 1, 0, 0, 0, 0, 0, 1 ]	1	448
22	[ 0, 1, 0, 0, 0, 0, 0 ]	6	64

Highest weight: [ 0, 0, 0, 0, 0, 1, 1 ]
Characteristic: 13
Dimension: 882

Level	dominant weight	weight multiplicity	length of W-orbit
35	[ 0, 0, 0, 0, 0, 1, 1 ]	1	168
31	[ 0, 0, 0, 0, 1, 0, 0 ]	2	280
13	[ 0, 0, 0, 0, 0, 0, 1 ]	11	14

Highest weight: [ 0, 0, 0, 0, 0, 1, 1 ]
Characteristic: not 3,13
Dimension: 896

Level	dominant weight	weight multiplicity	length of W-orbit
35	[ 0, 0, 0, 0, 0, 1, 1 ]	1	168
31	[ 0, 0, 0, 0, 1, 0, 0 ]	2	280
13	[ 0, 0, 0, 0, 0, 0, 1 ]	12	14

Highest weight: [ 0, 0, 0, 1, 0, 0, 0 ]
Characteristic: 2
Dimension: 910

Level	dominant weight	weight multiplicity	length of W-orbit
37	[ 0, 0, 0, 1, 0, 0, 0 ]	1	560
23	[ 0, 0, 0, 0, 0, 1, 0 ]	4	84
1	[ 0, 0, 0, 0, 0, 0, 0 ]	14	1

Highest weight: [ 0, 0, 0, 1, 0, 0, 0 ]
Characteristic: not 2
Dimension: 1001

Level	dominant weight	weight multiplicity	length of W-orbit
37	[ 0, 0, 0, 1, 0, 0, 0 ]	1	560
23	[ 0, 0, 0, 0, 0, 1, 0 ]	5	84
1	[ 0, 0, 0, 0, 0, 0, 0 ]	21	1

Highest weight: [ 0, 0, 1, 0, 0, 0, 0 ]
Characteristic: 2
Dimension: 1288

Level	dominant weight	weight multiplicity	length of W-orbit
41	[ 0, 0, 1, 0, 0, 0, 0 ]	1	672
31	[ 0, 0, 0, 0, 1, 0, 0 ]	2	280
13	[ 0, 0, 0, 0, 0, 0, 1 ]	4	14

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

Level	dominant weight	weight multiplicity	length of W-orbit
43	[ 0, 2, 0, 0, 0, 0, 0 ]	1	64
41	[ 0, 0, 1, 0, 0, 0, 0 ]	1	672
31	[ 0, 0, 0, 0, 1, 0, 0 ]	3	280
13	[ 0, 0, 0, 0, 0, 0, 1 ]	10	14

Highest weight: [ 2, 0, 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, 0 ]	1	64
41	[ 0, 0, 1, 0, 0, 0, 0 ]	1	672
31	[ 0, 0, 0, 0, 1, 0, 0 ]	3	280
13	[ 0, 0, 0, 0, 0, 0, 1 ]	10	14

Highest weight: [ 1, 1, 0, 0, 0, 0, 0 ]
Characteristic: 2
Dimension: 1912

Level	dominant weight	weight multiplicity	length of W-orbit
43	[ 1, 1, 0, 0, 0, 0, 0 ]	1	448
37	[ 0, 0, 0, 1, 0, 0, 0 ]	2	560
23	[ 0, 0, 0, 0, 0, 1, 0 ]	4	84
1	[ 0, 0, 0, 0, 0, 0, 0 ]	8	1

Highest weight: [ 0, 0, 0, 0, 0, 2, 0 ]
Characteristic: 3
Dimension: 1975

Level	dominant weight	weight multiplicity	length of W-orbit
45	[ 0, 0, 0, 0, 0, 2, 0 ]	1	84
43	[ 0, 0, 0, 0, 1, 0, 1 ]	1	840
37	[ 0, 0, 0, 1, 0, 0, 0 ]	1	560
25	[ 0, 0, 0, 0, 0, 0, 2 ]	4	14
23	[ 0, 0, 0, 0, 0, 1, 0 ]	5	84
1	[ 0, 0, 0, 0, 0, 0, 0 ]	15	1

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

Level	dominant weight	weight multiplicity	length of W-orbit
41	[ 0, 0, 1, 0, 0, 0, 0 ]	1	672
31	[ 0, 0, 0, 0, 1, 0, 0 ]	4	280
13	[ 0, 0, 0, 0, 0, 0, 1 ]	15	14

Highest weight: [ 0, 0, 0, 0, 0, 0, 4 ]
Characteristic: not 2,3
Dimension: 2275

Level	dominant weight	weight multiplicity	length of W-orbit
49	[ 0, 0, 0, 0, 0, 0, 4 ]	1	14
47	[ 0, 0, 0, 0, 0, 1, 2 ]	1	168
45	[ 0, 0, 0, 0, 0, 2, 0 ]	1	84
43	[ 0, 0, 0, 0, 1, 0, 1 ]	1	840
37	[ 0, 0, 0, 1, 0, 0, 0 ]	1	560
25	[ 0, 0, 0, 0, 0, 0, 2 ]	6	14
23	[ 0, 0, 0, 0, 0, 1, 0 ]	6	84
1	[ 0, 0, 0, 0, 0, 0, 0 ]	21	1

Highest weight: [ 0, 0, 0, 0, 1, 0, 1 ]
Characteristic: 2
Dimension: 2884

Level	dominant weight	weight multiplicity	length of W-orbit
43	[ 0, 0, 0, 0, 1, 0, 1 ]	1	840
37	[ 0, 0, 0, 1, 0, 0, 0 ]	2	560
25	[ 0, 0, 0, 0, 0, 0, 2 ]	4	14
23	[ 0, 0, 0, 0, 0, 1, 0 ]	10	84
1	[ 0, 0, 0, 0, 0, 0, 0 ]	28	1

Highest weight: [ 1, 1, 0, 0, 0, 0, 0 ]
Characteristic: not 2
Dimension: 3003

Level	dominant weight	weight multiplicity	length of W-orbit
43	[ 1, 1, 0, 0, 0, 0, 0 ]	1	448
37	[ 0, 0, 0, 1, 0, 0, 0 ]	3	560
23	[ 0, 0, 0, 0, 0, 1, 0 ]	10	84
1	[ 0, 0, 0, 0, 0, 0, 0 ]	35	1

Highest weight: [ 0, 0, 0, 0, 0, 2, 0 ]
Characteristic: 13
Dimension: 3079

Level	dominant weight	weight multiplicity	length of W-orbit
45	[ 0, 0, 0, 0, 0, 2, 0 ]	1	84
43	[ 0, 0, 0, 0, 1, 0, 1 ]	1	840
37	[ 0, 0, 0, 1, 0, 0, 0 ]	2	560
25	[ 0, 0, 0, 0, 0, 0, 2 ]	5	14
23	[ 0, 0, 0, 0, 0, 1, 0 ]	11	84
1	[ 0, 0, 0, 0, 0, 0, 0 ]	41	1

Highest weight: [ 0, 0, 0, 0, 0, 2, 0 ]
Characteristic: not 2,3,13
Dimension: 3080

Level	dominant weight	weight multiplicity	length of W-orbit
45	[ 0, 0, 0, 0, 0, 2, 0 ]	1	84
43	[ 0, 0, 0, 0, 1, 0, 1 ]	1	840
37	[ 0, 0, 0, 1, 0, 0, 0 ]	2	560
25	[ 0, 0, 0, 0, 0, 0, 2 ]	5	14
23	[ 0, 0, 0, 0, 0, 1, 0 ]	11	84
1	[ 0, 0, 0, 0, 0, 0, 0 ]	42	1

Highest weight: [ 0, 0, 0, 0, 1, 0, 1 ]
Characteristic: 3
Dimension: 3913

Level	dominant weight	weight multiplicity	length of W-orbit
43	[ 0, 0, 0, 0, 1, 0, 1 ]	1	840
37	[ 0, 0, 0, 1, 0, 0, 0 ]	3	560
25	[ 0, 0, 0, 0, 0, 0, 2 ]	6	14
23	[ 0, 0, 0, 0, 0, 1, 0 ]	15	84
1	[ 0, 0, 0, 0, 0, 0, 0 ]	49	1

Highest weight: [ 0, 0, 0, 0, 1, 0, 1 ]
Characteristic: not 2,3
Dimension: 4004

Level	dominant weight	weight multiplicity	length of W-orbit
43	[ 0, 0, 0, 0, 1, 0, 1 ]	1	840
37	[ 0, 0, 0, 1, 0, 0, 0 ]	3	560
25	[ 0, 0, 0, 0, 0, 0, 2 ]	6	14
23	[ 0, 0, 0, 0, 0, 1, 0 ]	16	84
1	[ 0, 0, 0, 0, 0, 0, 0 ]	56	1

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

Level	dominant weight	weight multiplicity	length of W-orbit
44	[ 0, 1, 0, 0, 0, 1, 0 ]	1	1344
34	[ 1, 0, 0, 0, 0, 0, 1 ]	4	448
22	[ 0, 1, 0, 0, 0, 0, 0 ]	15	64

Highest weight: [ 0, 1, 0, 0, 0, 1, 0 ]
Characteristic: 3
Dimension: 4096

Level	dominant weight	weight multiplicity	length of W-orbit
44	[ 0, 1, 0, 0, 0, 1, 0 ]	1	1344
34	[ 1, 0, 0, 0, 0, 0, 1 ]	4	448
22	[ 0, 1, 0, 0, 0, 0, 0 ]	15	64

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

Level	dominant weight	weight multiplicity	length of W-orbit
44	[ 1, 0, 0, 0, 0, 1, 0 ]	1	1344
34	[ 0, 1, 0, 0, 0, 0, 1 ]	4	448
22	[ 1, 0, 0, 0, 0, 0, 0 ]	15	64

Highest weight: [ 1, 0, 0, 0, 0, 1, 0 ]
Characteristic: 3
Dimension: 4096

Level	dominant weight	weight multiplicity	length of W-orbit
44	[ 1, 0, 0, 0, 0, 1, 0 ]	1	1344
34	[ 0, 1, 0, 0, 0, 0, 1 ]	4	448
22	[ 1, 0, 0, 0, 0, 0, 0 ]	15	64

Highest weight: [ 0, 1, 0, 0, 0, 1, 0 ]
Characteristic: 13
Dimension: 4864

Level	dominant weight	weight multiplicity	length of W-orbit
44	[ 0, 1, 0, 0, 0, 1, 0 ]	1	1344
34	[ 1, 0, 0, 0, 0, 0, 1 ]	5	448
22	[ 0, 1, 0, 0, 0, 0, 0 ]	20	64

Highest weight: [ 1, 0, 0, 0, 0, 1, 0 ]
Characteristic: 13
Dimension: 4864

Level	dominant weight	weight multiplicity	length of W-orbit
44	[ 1, 0, 0, 0, 0, 1, 0 ]	1	1344
34	[ 0, 1, 0, 0, 0, 0, 1 ]	5	448
22	[ 1, 0, 0, 0, 0, 0, 0 ]	20	64

Highest weight: [ 0, 1, 0, 0, 0, 1, 0 ]
Characteristic: not 2,3,13
Dimension: 4928

Level	dominant weight	weight multiplicity	length of W-orbit
44	[ 0, 1, 0, 0, 0, 1, 0 ]	1	1344
34	[ 1, 0, 0, 0, 0, 0, 1 ]	5	448
22	[ 0, 1, 0, 0, 0, 0, 0 ]	21	64

Highest weight: [ 1, 0, 0, 0, 0, 1, 0 ]
Characteristic: not 2,3,13
Dimension: 4928

Level	dominant weight	weight multiplicity	length of W-orbit
44	[ 1, 0, 0, 0, 0, 1, 0 ]	1	1344
34	[ 0, 1, 0, 0, 0, 0, 1 ]	5	448
22	[ 1, 0, 0, 0, 0, 0, 0 ]	21	64