[Overview]

Weight Multiplicities

Groups of type B7, degree bound 5000

Diagram:

1 < 2 - .. - 7

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 ]11

Highest weight: [ 0, 0, 0, 0, 0, 0, 1 ]
Characteristic: 2
Dimension: 14

Level   dominant weight   weight multiplicity   length of W-orbit 
15[ 0, 0, 0, 0, 0, 0, 1 ]114

Highest weight: [ 0, 0, 0, 0, 0, 0, 1 ]
Characteristic: not 2
Dimension: 15

Level   dominant weight   weight multiplicity   length of W-orbit 
15[ 0, 0, 0, 0, 0, 0, 1 ]114
1[ 0, 0, 0, 0, 0, 0, 0 ]11

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

Level   dominant weight   weight multiplicity   length of W-orbit 
27[ 0, 0, 0, 0, 0, 1, 0 ]184
1[ 0, 0, 0, 0, 0, 0, 0 ]61

Highest weight: [ 0, 0, 0, 0, 0, 1, 0 ]
Characteristic: not 2
Dimension: 105

Level   dominant weight   weight multiplicity   length of W-orbit 
27[ 0, 0, 0, 0, 0, 1, 0 ]184
15[ 0, 0, 0, 0, 0, 0, 1 ]114
1[ 0, 0, 0, 0, 0, 0, 0 ]71

Highest weight: [ 0, 0, 0, 0, 0, 0, 2 ]
Characteristic: 3
Dimension: 118

Level   dominant weight   weight multiplicity   length of W-orbit 
29[ 0, 0, 0, 0, 0, 0, 2 ]114
27[ 0, 0, 0, 0, 0, 1, 0 ]184
15[ 0, 0, 0, 0, 0, 0, 1 ]114
1[ 0, 0, 0, 0, 0, 0, 0 ]61

Highest weight: [ 0, 0, 0, 0, 0, 0, 2 ]
Characteristic: 5
Dimension: 118

Level   dominant weight   weight multiplicity   length of W-orbit 
29[ 0, 0, 0, 0, 0, 0, 2 ]114
27[ 0, 0, 0, 0, 0, 1, 0 ]184
15[ 0, 0, 0, 0, 0, 0, 1 ]114
1[ 0, 0, 0, 0, 0, 0, 0 ]61

Highest weight: [ 0, 0, 0, 0, 0, 0, 2 ]
Characteristic: not 2,3,5
Dimension: 119

Level   dominant weight   weight multiplicity   length of W-orbit 
29[ 0, 0, 0, 0, 0, 0, 2 ]114
27[ 0, 0, 0, 0, 0, 1, 0 ]184
15[ 0, 0, 0, 0, 0, 0, 1 ]114
1[ 0, 0, 0, 0, 0, 0, 0 ]71

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

Level   dominant weight   weight multiplicity   length of W-orbit 
29[ 1, 0, 0, 0, 0, 0, 0 ]1128

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

Level   dominant weight   weight multiplicity   length of W-orbit 
37[ 0, 0, 0, 0, 1, 0, 0 ]1280
15[ 0, 0, 0, 0, 0, 0, 1 ]414

Highest weight: [ 0, 0, 0, 0, 1, 0, 0 ]
Characteristic: not 2
Dimension: 455

Level   dominant weight   weight multiplicity   length of W-orbit 
37[ 0, 0, 0, 0, 1, 0, 0 ]1280
27[ 0, 0, 0, 0, 0, 1, 0 ]184
15[ 0, 0, 0, 0, 0, 0, 1 ]614
1[ 0, 0, 0, 0, 0, 0, 0 ]71

Highest weight: [ 0, 0, 0, 0, 0, 0, 3 ]
Characteristic: 17
Dimension: 650

Level   dominant weight   weight multiplicity   length of W-orbit 
43[ 0, 0, 0, 0, 0, 0, 3 ]114
41[ 0, 0, 0, 0, 0, 1, 1 ]1168
37[ 0, 0, 0, 0, 1, 0, 0 ]1280
29[ 0, 0, 0, 0, 0, 0, 2 ]114
27[ 0, 0, 0, 0, 0, 1, 0 ]184
15[ 0, 0, 0, 0, 0, 0, 1 ]614
1[ 0, 0, 0, 0, 0, 0, 0 ]61

Highest weight: [ 0, 0, 0, 0, 0, 1, 1 ]
Characteristic: 3
Dimension: 650

Level   dominant weight   weight multiplicity   length of W-orbit 
41[ 0, 0, 0, 0, 0, 1, 1 ]1168
37[ 0, 0, 0, 0, 1, 0, 0 ]1280
29[ 0, 0, 0, 0, 0, 0, 2 ]114
27[ 0, 0, 0, 0, 0, 1, 0 ]184
15[ 0, 0, 0, 0, 0, 0, 1 ]714
1[ 0, 0, 0, 0, 0, 0, 0 ]61

Highest weight: [ 0, 0, 0, 0, 0, 0, 3 ]
Characteristic: not 2,3,17
Dimension: 665

Level   dominant weight   weight multiplicity   length of W-orbit 
43[ 0, 0, 0, 0, 0, 0, 3 ]114
41[ 0, 0, 0, 0, 0, 1, 1 ]1168
37[ 0, 0, 0, 0, 1, 0, 0 ]1280
29[ 0, 0, 0, 0, 0, 0, 2 ]114
27[ 0, 0, 0, 0, 0, 1, 0 ]184
15[ 0, 0, 0, 0, 0, 0, 1 ]714
1[ 0, 0, 0, 0, 0, 0, 0 ]71

Highest weight: [ 0, 0, 0, 0, 0, 1, 1 ]
Characteristic: 2
Dimension: 896

Level   dominant weight   weight multiplicity   length of W-orbit 
41[ 0, 0, 0, 0, 0, 1, 1 ]1168
37[ 0, 0, 0, 0, 1, 0, 0 ]2280
15[ 0, 0, 0, 0, 0, 0, 1 ]1214

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

Level   dominant weight   weight multiplicity   length of W-orbit 
45[ 0, 0, 0, 1, 0, 0, 0 ]1560
27[ 0, 0, 0, 0, 0, 1, 0 ]484
1[ 0, 0, 0, 0, 0, 0, 0 ]141

Highest weight: [ 0, 0, 0, 0, 0, 1, 1 ]
Characteristic: 7
Dimension: 1090

Level   dominant weight   weight multiplicity   length of W-orbit 
41[ 0, 0, 0, 0, 0, 1, 1 ]1168
37[ 0, 0, 0, 0, 1, 0, 0 ]2280
29[ 0, 0, 0, 0, 0, 0, 2 ]114
27[ 0, 0, 0, 0, 0, 1, 0 ]284
15[ 0, 0, 0, 0, 0, 0, 1 ]1214
1[ 0, 0, 0, 0, 0, 0, 0 ]121

Highest weight: [ 0, 0, 0, 0, 0, 1, 1 ]
Characteristic: not 2,3,7
Dimension: 1105

Level   dominant weight   weight multiplicity   length of W-orbit 
41[ 0, 0, 0, 0, 0, 1, 1 ]1168
37[ 0, 0, 0, 0, 1, 0, 0 ]2280
29[ 0, 0, 0, 0, 0, 0, 2 ]114
27[ 0, 0, 0, 0, 0, 1, 0 ]284
15[ 0, 0, 0, 0, 0, 0, 1 ]1314
1[ 0, 0, 0, 0, 0, 0, 0 ]131

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

Level   dominant weight   weight multiplicity   length of W-orbit 
51[ 0, 0, 1, 0, 0, 0, 0 ]1672
37[ 0, 0, 0, 0, 1, 0, 0 ]2280
15[ 0, 0, 0, 0, 0, 0, 1 ]414

Highest weight: [ 0, 0, 0, 1, 0, 0, 0 ]
Characteristic: not 2
Dimension: 1365

Level   dominant weight   weight multiplicity   length of W-orbit 
45[ 0, 0, 0, 1, 0, 0, 0 ]1560
37[ 0, 0, 0, 0, 1, 0, 0 ]1280
27[ 0, 0, 0, 0, 0, 1, 0 ]584
15[ 0, 0, 0, 0, 0, 0, 1 ]614
1[ 0, 0, 0, 0, 0, 0, 0 ]211

Highest weight: [ 1, 0, 0, 0, 0, 0, 1 ]
Characteristic: 3
Dimension: 1664

Level   dominant weight   weight multiplicity   length of W-orbit 
43[ 1, 0, 0, 0, 0, 0, 1 ]1896
29[ 1, 0, 0, 0, 0, 0, 0 ]6128

Highest weight: [ 1, 0, 0, 0, 0, 0, 1 ]
Characteristic: 5
Dimension: 1664

Level   dominant weight   weight multiplicity   length of W-orbit 
43[ 1, 0, 0, 0, 0, 0, 1 ]1896
29[ 1, 0, 0, 0, 0, 0, 0 ]6128

Highest weight: [ 1, 0, 0, 0, 0, 0, 1 ]
Characteristic: not 3,5
Dimension: 1792

Level   dominant weight   weight multiplicity   length of W-orbit 
43[ 1, 0, 0, 0, 0, 0, 1 ]1896
29[ 1, 0, 0, 0, 0, 0, 0 ]7128

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

Level   dominant weight   weight multiplicity   length of W-orbit 
55[ 0, 1, 0, 0, 0, 0, 0 ]1448
45[ 0, 0, 0, 1, 0, 0, 0 ]2560
27[ 0, 0, 0, 0, 0, 1, 0 ]484
1[ 0, 0, 0, 0, 0, 0, 0 ]81

Highest weight: [ 0, 0, 0, 0, 0, 2, 0 ]
Characteristic: 3
Dimension: 2715

Level   dominant weight   weight multiplicity   length of W-orbit 
53[ 0, 0, 0, 0, 0, 2, 0 ]184
51[ 0, 0, 0, 0, 1, 0, 1 ]1840
45[ 0, 0, 0, 1, 0, 0, 0 ]1560
41[ 0, 0, 0, 0, 0, 1, 1 ]1168
37[ 0, 0, 0, 0, 1, 0, 0 ]1280
29[ 0, 0, 0, 0, 0, 0, 2 ]614
27[ 0, 0, 0, 0, 0, 1, 0 ]784
15[ 0, 0, 0, 0, 0, 0, 1 ]614
1[ 0, 0, 0, 0, 0, 0, 0 ]271

Highest weight: [ 0, 0, 0, 0, 0, 0, 4 ]
Characteristic: 19
Dimension: 2821

Level   dominant weight   weight multiplicity   length of W-orbit 
57[ 0, 0, 0, 0, 0, 0, 4 ]114
55[ 0, 0, 0, 0, 0, 1, 2 ]1168
53[ 0, 0, 0, 0, 0, 2, 0 ]184
51[ 0, 0, 0, 0, 1, 0, 1 ]1840
45[ 0, 0, 0, 1, 0, 0, 0 ]1560
43[ 0, 0, 0, 0, 0, 0, 3 ]114
41[ 0, 0, 0, 0, 0, 1, 1 ]1168
37[ 0, 0, 0, 0, 1, 0, 0 ]1280
29[ 0, 0, 0, 0, 0, 0, 2 ]614
27[ 0, 0, 0, 0, 0, 1, 0 ]684
15[ 0, 0, 0, 0, 0, 0, 1 ]614
1[ 0, 0, 0, 0, 0, 0, 0 ]211

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

Level   dominant weight   weight multiplicity   length of W-orbit 
51[ 0, 0, 0, 0, 1, 0, 1 ]1840
45[ 0, 0, 0, 1, 0, 0, 0 ]2560
29[ 0, 0, 0, 0, 0, 0, 2 ]414
27[ 0, 0, 0, 0, 0, 1, 0 ]1084
1[ 0, 0, 0, 0, 0, 0, 0 ]281

Highest weight: [ 0, 0, 0, 0, 0, 0, 4 ]
Characteristic: 17
Dimension: 2939

Level   dominant weight   weight multiplicity   length of W-orbit 
57[ 0, 0, 0, 0, 0, 0, 4 ]114
55[ 0, 0, 0, 0, 0, 1, 2 ]1168
53[ 0, 0, 0, 0, 0, 2, 0 ]184
51[ 0, 0, 0, 0, 1, 0, 1 ]1840
45[ 0, 0, 0, 1, 0, 0, 0 ]1560
43[ 0, 0, 0, 0, 0, 0, 3 ]114
41[ 0, 0, 0, 0, 0, 1, 1 ]1168
37[ 0, 0, 0, 0, 1, 0, 0 ]1280
29[ 0, 0, 0, 0, 0, 0, 2 ]714
27[ 0, 0, 0, 0, 0, 1, 0 ]784
15[ 0, 0, 0, 0, 0, 0, 1 ]714
1[ 0, 0, 0, 0, 0, 0, 0 ]271

Highest weight: [ 0, 0, 0, 0, 0, 0, 4 ]
Characteristic: not 2,3,17,19
Dimension: 2940

Level   dominant weight   weight multiplicity   length of W-orbit 
57[ 0, 0, 0, 0, 0, 0, 4 ]114
55[ 0, 0, 0, 0, 0, 1, 2 ]1168
53[ 0, 0, 0, 0, 0, 2, 0 ]184
51[ 0, 0, 0, 0, 1, 0, 1 ]1840
45[ 0, 0, 0, 1, 0, 0, 0 ]1560
43[ 0, 0, 0, 0, 0, 0, 3 ]114
41[ 0, 0, 0, 0, 0, 1, 1 ]1168
37[ 0, 0, 0, 0, 1, 0, 0 ]1280
29[ 0, 0, 0, 0, 0, 0, 2 ]714
27[ 0, 0, 0, 0, 0, 1, 0 ]784
15[ 0, 0, 0, 0, 0, 0, 1 ]714
1[ 0, 0, 0, 0, 0, 0, 0 ]281

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

Level   dominant weight   weight multiplicity   length of W-orbit 
51[ 0, 0, 1, 0, 0, 0, 0 ]1672
45[ 0, 0, 0, 1, 0, 0, 0 ]1560
37[ 0, 0, 0, 0, 1, 0, 0 ]4280
27[ 0, 0, 0, 0, 0, 1, 0 ]584
15[ 0, 0, 0, 0, 0, 0, 1 ]1514
1[ 0, 0, 0, 0, 0, 0, 0 ]211

Highest weight: [ 0, 0, 0, 0, 0, 2, 0 ]
Characteristic: 13
Dimension: 3961

Level   dominant weight   weight multiplicity   length of W-orbit 
53[ 0, 0, 0, 0, 0, 2, 0 ]184
51[ 0, 0, 0, 0, 1, 0, 1 ]1840
45[ 0, 0, 0, 1, 0, 0, 0 ]2560
41[ 0, 0, 0, 0, 0, 1, 1 ]1168
37[ 0, 0, 0, 0, 1, 0, 0 ]2280
29[ 0, 0, 0, 0, 0, 0, 2 ]514
27[ 0, 0, 0, 0, 0, 1, 0 ]1184
15[ 0, 0, 0, 0, 0, 0, 1 ]1114
1[ 0, 0, 0, 0, 0, 0, 0 ]411

Highest weight: [ 0, 0, 0, 0, 0, 2, 0 ]
Characteristic: 7
Dimension: 4079

Level   dominant weight   weight multiplicity   length of W-orbit 
53[ 0, 0, 0, 0, 0, 2, 0 ]184
51[ 0, 0, 0, 0, 1, 0, 1 ]1840
45[ 0, 0, 0, 1, 0, 0, 0 ]2560
41[ 0, 0, 0, 0, 0, 1, 1 ]1168
37[ 0, 0, 0, 0, 1, 0, 0 ]2280
29[ 0, 0, 0, 0, 0, 0, 2 ]614
27[ 0, 0, 0, 0, 0, 1, 0 ]1284
15[ 0, 0, 0, 0, 0, 0, 1 ]1214
1[ 0, 0, 0, 0, 0, 0, 0 ]471

Highest weight: [ 0, 0, 0, 0, 0, 2, 0 ]
Characteristic: not 2,3,7,13
Dimension: 4080

Level   dominant weight   weight multiplicity   length of W-orbit 
53[ 0, 0, 0, 0, 0, 2, 0 ]184
51[ 0, 0, 0, 0, 1, 0, 1 ]1840
45[ 0, 0, 0, 1, 0, 0, 0 ]2560
41[ 0, 0, 0, 0, 0, 1, 1 ]1168
37[ 0, 0, 0, 0, 1, 0, 0 ]2280
29[ 0, 0, 0, 0, 0, 0, 2 ]614
27[ 0, 0, 0, 0, 0, 1, 0 ]1284
15[ 0, 0, 0, 0, 0, 0, 1 ]1214
1[ 0, 0, 0, 0, 0, 0, 0 ]481