Weight Multiplicities

Groups of type E7, degree bound 100000

Diagram:

         2
         |
 1 - 3 - 4 - 5 - 6 - 7

Overview

Dimension	Highest weight	Characteristic
1	[ 0, 0, 0, 0, 0, 0, 0 ]	all
56	[ 0, 0, 0, 0, 0, 0, 1 ]	all
132	[ 1, 0, 0, 0, 0, 0, 0 ]	2
133	[ 1, 0, 0, 0, 0, 0, 0 ]	not 2
856	[ 0, 1, 0, 0, 0, 0, 0 ]	3
912	[ 0, 1, 0, 0, 0, 0, 0 ]	not 3
1274	[ 0, 0, 0, 0, 0, 1, 0 ]	2
1330	[ 0, 0, 0, 0, 0, 0, 2 ]	3
1463	[ 0, 0, 0, 0, 0, 0, 2 ]	not 2, 3
1538	[ 0, 0, 0, 0, 0, 1, 0 ]	7
1539	[ 0, 0, 0, 0, 0, 1, 0 ]	not 2, 7
5568	[ 1, 0, 0, 0, 0, 0, 1 ]	7
5832	[ 2, 0, 0, 0, 0, 0, 0 ]	5
6424	[ 1, 0, 0, 0, 0, 0, 1 ]	19
6480	[ 1, 0, 0, 0, 0, 0, 1 ]	not 7, 19
7106	[ 0, 0, 1, 0, 0, 0, 0 ]	2
7370	[ 2, 0, 0, 0, 0, 0, 0 ]	19
7371	[ 2, 0, 0, 0, 0, 0, 0 ]	not 2, 5, 19
8512	[ 0, 0, 1, 0, 0, 0, 0 ]	3
8645	[ 0, 0, 1, 0, 0, 0, 0 ]	not 2, 3
18752	[ 0, 0, 0, 0, 0, 0, 3 ]	7
21184	[ 0, 0, 0, 0, 1, 0, 0 ]	2
24264	[ 0, 0, 0, 0, 0, 0, 3 ]	11
24264	[ 0, 0, 0, 0, 0, 1, 1 ]	3
24320	[ 0, 0, 0, 0, 0, 0, 3 ]	not 2, 3, 7, 11
25896	[ 0, 0, 0, 0, 1, 0, 0 ]	3
27664	[ 0, 0, 0, 0, 1, 0, 0 ]	not 2, 3
30704	[ 0, 1, 0, 0, 0, 0, 1 ]	2
30779	[ 0, 1, 0, 0, 0, 0, 1 ]	3
39217	[ 0, 1, 0, 0, 0, 0, 1 ]	7
40755	[ 0, 1, 0, 0, 0, 0, 1 ]	not 2, 3, 7
44592	[ 0, 0, 0, 0, 0, 1, 1 ]	11
50160	[ 0, 0, 0, 0, 0, 1, 1 ]	2
51072	[ 0, 0, 0, 0, 0, 1, 1 ]	not 2, 3, 11
57608	[ 1, 1, 0, 0, 0, 0, 0 ]	5
79704	[ 1, 1, 0, 0, 0, 0, 0 ]	13
86128	[ 1, 1, 0, 0, 0, 0, 0 ]	2
86184	[ 1, 1, 0, 0, 0, 0, 0 ]	not 2, 5, 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: 56

Level	dominant weight	weight multiplicity	length of W-orbit
28	[ 0, 0, 0, 0, 0, 0, 1 ]	1	56

Highest weight: [ 1, 0, 0, 0, 0, 0, 0 ]
Characteristic: 2
Dimension: 132

Level	dominant weight	weight multiplicity	length of W-orbit
35	[ 1, 0, 0, 0, 0, 0, 0 ]	1	126
1	[ 0, 0, 0, 0, 0, 0, 0 ]	6	1

Highest weight: [ 1, 0, 0, 0, 0, 0, 0 ]
Characteristic: not 2
Dimension: 133

Level	dominant weight	weight multiplicity	length of W-orbit
35	[ 1, 0, 0, 0, 0, 0, 0 ]	1	126
1	[ 0, 0, 0, 0, 0, 0, 0 ]	7	1

Highest weight: [ 0, 1, 0, 0, 0, 0, 0 ]
Characteristic: 3
Dimension: 856

Level	dominant weight	weight multiplicity	length of W-orbit
50	[ 0, 1, 0, 0, 0, 0, 0 ]	1	576
28	[ 0, 0, 0, 0, 0, 0, 1 ]	5	56

Highest weight: [ 0, 1, 0, 0, 0, 0, 0 ]
Characteristic: not 3
Dimension: 912

Level	dominant weight	weight multiplicity	length of W-orbit
50	[ 0, 1, 0, 0, 0, 0, 0 ]	1	576
28	[ 0, 0, 0, 0, 0, 0, 1 ]	6	56

Highest weight: [ 0, 0, 0, 0, 0, 1, 0 ]
Characteristic: 2
Dimension: 1274

Level	dominant weight	weight multiplicity	length of W-orbit
53	[ 0, 0, 0, 0, 0, 1, 0 ]	1	756
35	[ 1, 0, 0, 0, 0, 0, 0 ]	4	126
1	[ 0, 0, 0, 0, 0, 0, 0 ]	14	1

Highest weight: [ 0, 0, 0, 0, 0, 0, 2 ]
Characteristic: 3
Dimension: 1330

Level	dominant weight	weight multiplicity	length of W-orbit
55	[ 0, 0, 0, 0, 0, 0, 2 ]	1	56
53	[ 0, 0, 0, 0, 0, 1, 0 ]	1	756
35	[ 1, 0, 0, 0, 0, 0, 0 ]	4	126
1	[ 0, 0, 0, 0, 0, 0, 0 ]	14	1

Highest weight: [ 0, 0, 0, 0, 0, 0, 2 ]
Characteristic: not 2,3
Dimension: 1463

Level	dominant weight	weight multiplicity	length of W-orbit
55	[ 0, 0, 0, 0, 0, 0, 2 ]	1	56
53	[ 0, 0, 0, 0, 0, 1, 0 ]	1	756
35	[ 1, 0, 0, 0, 0, 0, 0 ]	5	126
1	[ 0, 0, 0, 0, 0, 0, 0 ]	21	1

Highest weight: [ 0, 0, 0, 0, 0, 1, 0 ]
Characteristic: 7
Dimension: 1538

Level	dominant weight	weight multiplicity	length of W-orbit
53	[ 0, 0, 0, 0, 0, 1, 0 ]	1	756
35	[ 1, 0, 0, 0, 0, 0, 0 ]	6	126
1	[ 0, 0, 0, 0, 0, 0, 0 ]	26	1

Highest weight: [ 0, 0, 0, 0, 0, 1, 0 ]
Characteristic: not 2,7
Dimension: 1539

Level	dominant weight	weight multiplicity	length of W-orbit
53	[ 0, 0, 0, 0, 0, 1, 0 ]	1	756
35	[ 1, 0, 0, 0, 0, 0, 0 ]	6	126
1	[ 0, 0, 0, 0, 0, 0, 0 ]	27	1

Highest weight: [ 1, 0, 0, 0, 0, 0, 1 ]
Characteristic: 7
Dimension: 5568

Level	dominant weight	weight multiplicity	length of W-orbit
62	[ 1, 0, 0, 0, 0, 0, 1 ]	1	1512
50	[ 0, 1, 0, 0, 0, 0, 0 ]	5	576
28	[ 0, 0, 0, 0, 0, 0, 1 ]	21	56

Highest weight: [ 2, 0, 0, 0, 0, 0, 0 ]
Characteristic: 5
Dimension: 5832

Level	dominant weight	weight multiplicity	length of W-orbit
69	[ 2, 0, 0, 0, 0, 0, 0 ]	1	126
67	[ 0, 0, 1, 0, 0, 0, 0 ]	1	2016
53	[ 0, 0, 0, 0, 0, 1, 0 ]	3	756
35	[ 1, 0, 0, 0, 0, 0, 0 ]	11	126
1	[ 0, 0, 0, 0, 0, 0, 0 ]	36	1

Highest weight: [ 1, 0, 0, 0, 0, 0, 1 ]
Characteristic: 19
Dimension: 6424

Level	dominant weight	weight multiplicity	length of W-orbit
62	[ 1, 0, 0, 0, 0, 0, 1 ]	1	1512
50	[ 0, 1, 0, 0, 0, 0, 0 ]	6	576
28	[ 0, 0, 0, 0, 0, 0, 1 ]	26	56

Highest weight: [ 1, 0, 0, 0, 0, 0, 1 ]
Characteristic: not 7,19
Dimension: 6480

Level	dominant weight	weight multiplicity	length of W-orbit
62	[ 1, 0, 0, 0, 0, 0, 1 ]	1	1512
50	[ 0, 1, 0, 0, 0, 0, 0 ]	6	576
28	[ 0, 0, 0, 0, 0, 0, 1 ]	27	56

Highest weight: [ 0, 0, 1, 0, 0, 0, 0 ]
Characteristic: 2
Dimension: 7106

Level	dominant weight	weight multiplicity	length of W-orbit
67	[ 0, 0, 1, 0, 0, 0, 0 ]	1	2016
53	[ 0, 0, 0, 0, 0, 1, 0 ]	4	756
35	[ 1, 0, 0, 0, 0, 0, 0 ]	16	126
1	[ 0, 0, 0, 0, 0, 0, 0 ]	50	1

Highest weight: [ 2, 0, 0, 0, 0, 0, 0 ]
Characteristic: 19
Dimension: 7370

Level	dominant weight	weight multiplicity	length of W-orbit
69	[ 2, 0, 0, 0, 0, 0, 0 ]	1	126
67	[ 0, 0, 1, 0, 0, 0, 0 ]	1	2016
53	[ 0, 0, 0, 0, 0, 1, 0 ]	4	756
35	[ 1, 0, 0, 0, 0, 0, 0 ]	17	126
1	[ 0, 0, 0, 0, 0, 0, 0 ]	62	1

Highest weight: [ 2, 0, 0, 0, 0, 0, 0 ]
Characteristic: not 2,5,19
Dimension: 7371

Level	dominant weight	weight multiplicity	length of W-orbit
69	[ 2, 0, 0, 0, 0, 0, 0 ]	1	126
67	[ 0, 0, 1, 0, 0, 0, 0 ]	1	2016
53	[ 0, 0, 0, 0, 0, 1, 0 ]	4	756
35	[ 1, 0, 0, 0, 0, 0, 0 ]	17	126
1	[ 0, 0, 0, 0, 0, 0, 0 ]	63	1

Highest weight: [ 0, 0, 1, 0, 0, 0, 0 ]
Characteristic: 3
Dimension: 8512

Level	dominant weight	weight multiplicity	length of W-orbit
67	[ 0, 0, 1, 0, 0, 0, 0 ]	1	2016
53	[ 0, 0, 0, 0, 0, 1, 0 ]	5	756
35	[ 1, 0, 0, 0, 0, 0, 0 ]	21	126
1	[ 0, 0, 0, 0, 0, 0, 0 ]	70	1

Highest weight: [ 0, 0, 1, 0, 0, 0, 0 ]
Characteristic: not 2,3
Dimension: 8645

Level	dominant weight	weight multiplicity	length of W-orbit
67	[ 0, 0, 1, 0, 0, 0, 0 ]	1	2016
53	[ 0, 0, 0, 0, 0, 1, 0 ]	5	756
35	[ 1, 0, 0, 0, 0, 0, 0 ]	22	126
1	[ 0, 0, 0, 0, 0, 0, 0 ]	77	1

Highest weight: [ 0, 0, 0, 0, 0, 0, 3 ]
Characteristic: 7
Dimension: 18752

Level	dominant weight	weight multiplicity	length of W-orbit
82	[ 0, 0, 0, 0, 0, 0, 3 ]	1	56
80	[ 0, 0, 0, 0, 0, 1, 1 ]	1	1512
76	[ 0, 0, 0, 0, 1, 0, 0 ]	1	4032
62	[ 1, 0, 0, 0, 0, 0, 1 ]	4	1512
50	[ 0, 1, 0, 0, 0, 0, 0 ]	10	576
28	[ 0, 0, 0, 0, 0, 0, 1 ]	24	56

Highest weight: [ 0, 0, 0, 0, 1, 0, 0 ]
Characteristic: 2
Dimension: 21184

Level	dominant weight	weight multiplicity	length of W-orbit
76	[ 0, 0, 0, 0, 1, 0, 0 ]	1	4032
62	[ 1, 0, 0, 0, 0, 0, 1 ]	4	1512
50	[ 0, 1, 0, 0, 0, 0, 0 ]	15	576
28	[ 0, 0, 0, 0, 0, 0, 1 ]	44	56

Highest weight: [ 0, 0, 0, 0, 0, 0, 3 ]
Characteristic: 11
Dimension: 24264

Level	dominant weight	weight multiplicity	length of W-orbit
82	[ 0, 0, 0, 0, 0, 0, 3 ]	1	56
80	[ 0, 0, 0, 0, 0, 1, 1 ]	1	1512
76	[ 0, 0, 0, 0, 1, 0, 0 ]	1	4032
62	[ 1, 0, 0, 0, 0, 0, 1 ]	5	1512
50	[ 0, 1, 0, 0, 0, 0, 0 ]	15	576
28	[ 0, 0, 0, 0, 0, 0, 1 ]	44	56

Highest weight: [ 0, 0, 0, 0, 0, 1, 1 ]
Characteristic: 3
Dimension: 24264

Level	dominant weight	weight multiplicity	length of W-orbit
80	[ 0, 0, 0, 0, 0, 1, 1 ]	1	1512
76	[ 0, 0, 0, 0, 1, 0, 0 ]	1	4032
62	[ 1, 0, 0, 0, 0, 0, 1 ]	5	1512
50	[ 0, 1, 0, 0, 0, 0, 0 ]	15	576
28	[ 0, 0, 0, 0, 0, 0, 1 ]	45	56

Highest weight: [ 0, 0, 0, 0, 0, 0, 3 ]
Characteristic: not 2,3,7,11
Dimension: 24320

Level	dominant weight	weight multiplicity	length of W-orbit
82	[ 0, 0, 0, 0, 0, 0, 3 ]	1	56
80	[ 0, 0, 0, 0, 0, 1, 1 ]	1	1512
76	[ 0, 0, 0, 0, 1, 0, 0 ]	1	4032
62	[ 1, 0, 0, 0, 0, 0, 1 ]	5	1512
50	[ 0, 1, 0, 0, 0, 0, 0 ]	15	576
28	[ 0, 0, 0, 0, 0, 0, 1 ]	45	56

Highest weight: [ 0, 0, 0, 0, 1, 0, 0 ]
Characteristic: 3
Dimension: 25896

Level	dominant weight	weight multiplicity	length of W-orbit
76	[ 0, 0, 0, 0, 1, 0, 0 ]	1	4032
62	[ 1, 0, 0, 0, 0, 0, 1 ]	5	1512
50	[ 0, 1, 0, 0, 0, 0, 0 ]	19	576
28	[ 0, 0, 0, 0, 0, 0, 1 ]	60	56

Highest weight: [ 0, 0, 0, 0, 1, 0, 0 ]
Characteristic: not 2,3
Dimension: 27664

Level	dominant weight	weight multiplicity	length of W-orbit
76	[ 0, 0, 0, 0, 1, 0, 0 ]	1	4032
62	[ 1, 0, 0, 0, 0, 0, 1 ]	5	1512
50	[ 0, 1, 0, 0, 0, 0, 0 ]	21	576
28	[ 0, 0, 0, 0, 0, 0, 1 ]	71	56

Highest weight: [ 0, 1, 0, 0, 0, 0, 1 ]
Characteristic: 2
Dimension: 30704

Level	dominant weight	weight multiplicity	length of W-orbit
77	[ 0, 1, 0, 0, 0, 0, 1 ]	1	4032
67	[ 0, 0, 1, 0, 0, 0, 0 ]	4	2016
55	[ 0, 0, 0, 0, 0, 0, 2 ]	6	56
53	[ 0, 0, 0, 0, 0, 1, 0 ]	16	756
35	[ 1, 0, 0, 0, 0, 0, 0 ]	48	126
1	[ 0, 0, 0, 0, 0, 0, 0 ]	128	1

Highest weight: [ 0, 1, 0, 0, 0, 0, 1 ]
Characteristic: 3
Dimension: 30779

Level	dominant weight	weight multiplicity	length of W-orbit
77	[ 0, 1, 0, 0, 0, 0, 1 ]	1	4032
67	[ 0, 0, 1, 0, 0, 0, 0 ]	4	2016
55	[ 0, 0, 0, 0, 0, 0, 2 ]	5	56
53	[ 0, 0, 0, 0, 0, 1, 0 ]	16	756
35	[ 1, 0, 0, 0, 0, 0, 0 ]	49	126
1	[ 0, 0, 0, 0, 0, 0, 0 ]	133	1

Highest weight: [ 0, 1, 0, 0, 0, 0, 1 ]
Characteristic: 7
Dimension: 39217

Level	dominant weight	weight multiplicity	length of W-orbit
77	[ 0, 1, 0, 0, 0, 0, 1 ]	1	4032
67	[ 0, 0, 1, 0, 0, 0, 0 ]	5	2016
55	[ 0, 0, 0, 0, 0, 0, 2 ]	6	56
53	[ 0, 0, 0, 0, 0, 1, 0 ]	21	756
35	[ 1, 0, 0, 0, 0, 0, 0 ]	69	126
1	[ 0, 0, 0, 0, 0, 0, 0 ]	199	1

Highest weight: [ 0, 1, 0, 0, 0, 0, 1 ]
Characteristic: not 2,3,7
Dimension: 40755

Level	dominant weight	weight multiplicity	length of W-orbit
77	[ 0, 1, 0, 0, 0, 0, 1 ]	1	4032
67	[ 0, 0, 1, 0, 0, 0, 0 ]	5	2016
55	[ 0, 0, 0, 0, 0, 0, 2 ]	6	56
53	[ 0, 0, 0, 0, 0, 1, 0 ]	22	756
35	[ 1, 0, 0, 0, 0, 0, 0 ]	75	126
1	[ 0, 0, 0, 0, 0, 0, 0 ]	225	1

Highest weight: [ 0, 0, 0, 0, 0, 1, 1 ]
Characteristic: 11
Dimension: 44592

Level	dominant weight	weight multiplicity	length of W-orbit
80	[ 0, 0, 0, 0, 0, 1, 1 ]	1	1512
76	[ 0, 0, 0, 0, 1, 0, 0 ]	2	4032
62	[ 1, 0, 0, 0, 0, 0, 1 ]	9	1512
50	[ 0, 1, 0, 0, 0, 0, 0 ]	29	576
28	[ 0, 0, 0, 0, 0, 0, 1 ]	84	56

Highest weight: [ 0, 0, 0, 0, 0, 1, 1 ]
Characteristic: 2
Dimension: 50160

Level	dominant weight	weight multiplicity	length of W-orbit
80	[ 0, 0, 0, 0, 0, 1, 1 ]	1	1512
76	[ 0, 0, 0, 0, 1, 0, 0 ]	2	4032
62	[ 1, 0, 0, 0, 0, 0, 1 ]	10	1512
50	[ 0, 1, 0, 0, 0, 0, 0 ]	34	576
28	[ 0, 0, 0, 0, 0, 0, 1 ]	105	56

Highest weight: [ 0, 0, 0, 0, 0, 1, 1 ]
Characteristic: not 2,3,11
Dimension: 51072

Level	dominant weight	weight multiplicity	length of W-orbit
80	[ 0, 0, 0, 0, 0, 1, 1 ]	1	1512
76	[ 0, 0, 0, 0, 1, 0, 0 ]	2	4032
62	[ 1, 0, 0, 0, 0, 0, 1 ]	10	1512
50	[ 0, 1, 0, 0, 0, 0, 0 ]	35	576
28	[ 0, 0, 0, 0, 0, 0, 1 ]	111	56

Highest weight: [ 1, 1, 0, 0, 0, 0, 0 ]
Characteristic: 5
Dimension: 57608

Level	dominant weight	weight multiplicity	length of W-orbit
84	[ 1, 1, 0, 0, 0, 0, 0 ]	1	4032
76	[ 0, 0, 0, 0, 1, 0, 0 ]	3	4032
62	[ 1, 0, 0, 0, 0, 0, 1 ]	11	1512
50	[ 0, 1, 0, 0, 0, 0, 0 ]	34	576
28	[ 0, 0, 0, 0, 0, 0, 1 ]	94	56

Highest weight: [ 1, 1, 0, 0, 0, 0, 0 ]
Characteristic: 13
Dimension: 79704

Level	dominant weight	weight multiplicity	length of W-orbit
84	[ 1, 1, 0, 0, 0, 0, 0 ]	1	4032
76	[ 0, 0, 0, 0, 1, 0, 0 ]	4	4032
62	[ 1, 0, 0, 0, 0, 0, 1 ]	15	1512
50	[ 0, 1, 0, 0, 0, 0, 0 ]	50	576
28	[ 0, 0, 0, 0, 0, 0, 1 ]	144	56

Highest weight: [ 1, 1, 0, 0, 0, 0, 0 ]
Characteristic: 2
Dimension: 86128

Level	dominant weight	weight multiplicity	length of W-orbit
84	[ 1, 1, 0, 0, 0, 0, 0 ]	1	4032
76	[ 0, 0, 0, 0, 1, 0, 0 ]	4	4032
62	[ 1, 0, 0, 0, 0, 0, 1 ]	16	1512
50	[ 0, 1, 0, 0, 0, 0, 0 ]	56	576
28	[ 0, 0, 0, 0, 0, 0, 1 ]	170	56

Highest weight: [ 1, 1, 0, 0, 0, 0, 0 ]
Characteristic: not 2,5,13
Dimension: 86184

Level	dominant weight	weight multiplicity	length of W-orbit
84	[ 1, 1, 0, 0, 0, 0, 0 ]	1	4032
76	[ 0, 0, 0, 0, 1, 0, 0 ]	4	4032
62	[ 1, 0, 0, 0, 0, 0, 1 ]	16	1512
50	[ 0, 1, 0, 0, 0, 0, 0 ]	56	576
28	[ 0, 0, 0, 0, 0, 0, 1 ]	171	56