[Overview]

Weight Multiplicities

Groups of type B4, all 2-restricted weight in characteristic 2

Diagram:

1 < 2 - 3 - 4

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

Level   dominant weight   weight multiplicity   length of W-orbit 
1[ 0, 0, 0, 0 ]11

Highest weight: [ 0, 0, 0, 1 ]
Characteristic: 2
Dimension: 8

Level   dominant weight   weight multiplicity   length of W-orbit 
9[ 0, 0, 0, 1 ]18

Highest weight: [ 1, 0, 0, 0 ]
Characteristic: 2
Dimension: 16

Level   dominant weight   weight multiplicity   length of W-orbit 
11[ 1, 0, 0, 0 ]116

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

Level   dominant weight   weight multiplicity   length of W-orbit 
15[ 0, 0, 1, 0 ]124
1[ 0, 0, 0, 0 ]21

Highest weight: [ 0, 1, 0, 0 ]
Characteristic: 2
Dimension: 48

Level   dominant weight   weight multiplicity   length of W-orbit 
19[ 0, 1, 0, 0 ]132
9[ 0, 0, 0, 1 ]28

Highest weight: [ 1, 0, 0, 1 ]
Characteristic: 2
Dimension: 128

Level   dominant weight   weight multiplicity   length of W-orbit 
19[ 1, 0, 0, 1 ]164
11[ 1, 0, 0, 0 ]416

Highest weight: [ 0, 0, 1, 1 ]
Characteristic: 2
Dimension: 160

Level   dominant weight   weight multiplicity   length of W-orbit 
23[ 0, 0, 1, 1 ]148
19[ 0, 1, 0, 0 ]232
9[ 0, 0, 0, 1 ]68

Highest weight: [ 1, 0, 1, 0 ]
Characteristic: 2
Dimension: 416

Level   dominant weight   weight multiplicity   length of W-orbit 
25[ 1, 0, 1, 0 ]196
19[ 1, 0, 0, 1 ]364
11[ 1, 0, 0, 0 ]816

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

Level   dominant weight   weight multiplicity   length of W-orbit 
27[ 0, 1, 0, 1 ]196
21[ 2, 0, 0, 0 ]216
17[ 0, 0, 0, 2 ]28
15[ 0, 0, 1, 0 ]424
1[ 0, 0, 0, 0 ]61

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

Level   dominant weight   weight multiplicity   length of W-orbit 
29[ 1, 1, 0, 0 ]164
25[ 1, 0, 1, 0 ]296
19[ 1, 0, 0, 1 ]564
11[ 1, 0, 0, 0 ]1216

Highest weight: [ 0, 1, 1, 0 ]
Characteristic: 2
Dimension: 784

Level   dominant weight   weight multiplicity   length of W-orbit 
33[ 0, 1, 1, 0 ]196
29[ 2, 0, 0, 1 ]264
23[ 0, 0, 1, 1 ]448
19[ 0, 1, 0, 0 ]832
9[ 0, 0, 0, 1 ]148

Highest weight: [ 1, 0, 1, 1 ]
Characteristic: 2
Dimension: 2560

Level   dominant weight   weight multiplicity   length of W-orbit 
33[ 1, 0, 1, 1 ]1192
29[ 1, 1, 0, 0 ]264
27[ 1, 0, 0, 2 ]364
25[ 1, 0, 1, 0 ]696
19[ 1, 0, 0, 1 ]1564
11[ 1, 0, 0, 0 ]3216

Highest weight: [ 1, 1, 0, 1 ]
Characteristic: 2
Dimension: 3936

Level   dominant weight   weight multiplicity   length of W-orbit 
37[ 1, 1, 0, 1 ]1192
33[ 1, 0, 1, 1 ]2192
31[ 3, 0, 0, 0 ]216
29[ 1, 1, 0, 0 ]564
27[ 1, 0, 0, 2 ]564
25[ 1, 0, 1, 0 ]1096
19[ 1, 0, 0, 1 ]1964
11[ 1, 0, 0, 0 ]3216

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

Level   dominant weight   weight multiplicity   length of W-orbit 
41[ 0, 1, 1, 1 ]1192
37[ 2, 0, 0, 2 ]264
37[ 0, 2, 0, 0 ]232
35[ 2, 0, 1, 0 ]496
31[ 0, 0, 1, 2 ]448
29[ 0, 0, 2, 0 ]824
27[ 0, 1, 0, 1 ]1496
21[ 2, 0, 0, 0 ]2416
17[ 0, 0, 0, 2 ]248
15[ 0, 0, 1, 0 ]4024
1[ 0, 0, 0, 0 ]641

Highest weight: [ 1, 1, 1, 0 ]
Characteristic: 2
Dimension: 12544

Level   dominant weight   weight multiplicity   length of W-orbit 
43[ 1, 1, 1, 0 ]1192
39[ 3, 0, 0, 1 ]264
39[ 1, 0, 2, 0 ]296
37[ 1, 1, 0, 1 ]4192
33[ 1, 0, 1, 1 ]8192
31[ 3, 0, 0, 0 ]816
29[ 1, 1, 0, 0 ]1764
27[ 1, 0, 0, 2 ]1464
25[ 1, 0, 1, 0 ]3096
19[ 1, 0, 0, 1 ]5264
11[ 1, 0, 0, 0 ]8816

Highest weight: [ 1, 1, 1, 1 ]
Characteristic: 2
Dimension: 65536

Level   dominant weight   weight multiplicity   length of W-orbit 
51[ 1, 1, 1, 1 ]1384
47[ 3, 0, 0, 2 ]264
47[ 1, 2, 0, 0 ]264
47[ 1, 0, 2, 1 ]2192
45[ 3, 0, 1, 0 ]496
45[ 1, 1, 0, 2 ]4192
43[ 1, 1, 1, 0 ]8192
41[ 1, 0, 1, 2 ]8192
39[ 3, 0, 0, 1 ]1464
39[ 1, 0, 2, 0 ]1696
37[ 1, 1, 0, 1 ]28192
35[ 1, 0, 0, 3 ]1464
33[ 1, 0, 1, 1 ]48192
31[ 3, 0, 0, 0 ]4816
29[ 1, 1, 0, 0 ]8064
27[ 1, 0, 0, 2 ]8064
25[ 1, 0, 1, 0 ]13296
19[ 1, 0, 0, 1 ]21064
11[ 1, 0, 0, 0 ]32816