[Overview]

Weight Multiplicities

Groups of type B9, degree bound 8000

Diagram:

1 < 2 - .. - 9

Highest weight: [ 0, 0, 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, 0, 0 ]11

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ]
Characteristic: 2
Dimension: 18

Level   dominant weight   weight multiplicity   length of W-orbit 
19[ 0, 0, 0, 0, 0, 0, 0, 0, 1 ]118

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ]
Characteristic: not 2
Dimension: 19

Level   dominant weight   weight multiplicity   length of W-orbit 
19[ 0, 0, 0, 0, 0, 0, 0, 0, 1 ]118
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0 ]11

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ]
Characteristic: 2
Dimension: 152

Level   dominant weight   weight multiplicity   length of W-orbit 
35[ 0, 0, 0, 0, 0, 0, 0, 1, 0 ]1144
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0 ]81

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ]
Characteristic: not 2
Dimension: 171

Level   dominant weight   weight multiplicity   length of W-orbit 
35[ 0, 0, 0, 0, 0, 0, 0, 1, 0 ]1144
19[ 0, 0, 0, 0, 0, 0, 0, 0, 1 ]118
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0 ]91

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 2 ]
Characteristic: 19
Dimension: 188

Level   dominant weight   weight multiplicity   length of W-orbit 
37[ 0, 0, 0, 0, 0, 0, 0, 0, 2 ]118
35[ 0, 0, 0, 0, 0, 0, 0, 1, 0 ]1144
19[ 0, 0, 0, 0, 0, 0, 0, 0, 1 ]118
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0 ]81

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 2 ]
Characteristic: not 2,19
Dimension: 189

Level   dominant weight   weight multiplicity   length of W-orbit 
37[ 0, 0, 0, 0, 0, 0, 0, 0, 2 ]118
35[ 0, 0, 0, 0, 0, 0, 0, 1, 0 ]1144
19[ 0, 0, 0, 0, 0, 0, 0, 0, 1 ]118
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0 ]91

Highest weight: [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ]
Characteristic: all
Dimension: 512

Level   dominant weight   weight multiplicity   length of W-orbit 
46[ 1, 0, 0, 0, 0, 0, 0, 0, 0 ]1512

Highest weight: [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ]
Characteristic: 2
Dimension: 780

Level   dominant weight   weight multiplicity   length of W-orbit 
49[ 0, 0, 0, 0, 0, 0, 1, 0, 0 ]1672
19[ 0, 0, 0, 0, 0, 0, 0, 0, 1 ]618

Highest weight: [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ]
Characteristic: not 2
Dimension: 969

Level   dominant weight   weight multiplicity   length of W-orbit 
49[ 0, 0, 0, 0, 0, 0, 1, 0, 0 ]1672
35[ 0, 0, 0, 0, 0, 0, 0, 1, 0 ]1144
19[ 0, 0, 0, 0, 0, 0, 0, 0, 1 ]818
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0 ]91

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 1, 1 ]
Characteristic: 3
Dimension: 1273

Level   dominant weight   weight multiplicity   length of W-orbit 
53[ 0, 0, 0, 0, 0, 0, 0, 1, 1 ]1288
49[ 0, 0, 0, 0, 0, 0, 1, 0, 0 ]1672
37[ 0, 0, 0, 0, 0, 0, 0, 0, 2 ]118
35[ 0, 0, 0, 0, 0, 0, 0, 1, 0 ]1144
19[ 0, 0, 0, 0, 0, 0, 0, 0, 1 ]818
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0 ]71

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 3 ]
Characteristic: 7
Dimension: 1292

Level   dominant weight   weight multiplicity   length of W-orbit 
55[ 0, 0, 0, 0, 0, 0, 0, 0, 3 ]118
53[ 0, 0, 0, 0, 0, 0, 0, 1, 1 ]1288
49[ 0, 0, 0, 0, 0, 0, 1, 0, 0 ]1672
37[ 0, 0, 0, 0, 0, 0, 0, 0, 2 ]118
35[ 0, 0, 0, 0, 0, 0, 0, 1, 0 ]1144
19[ 0, 0, 0, 0, 0, 0, 0, 0, 1 ]818
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0 ]81

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 3 ]
Characteristic: not 2,3,7
Dimension: 1311

Level   dominant weight   weight multiplicity   length of W-orbit 
55[ 0, 0, 0, 0, 0, 0, 0, 0, 3 ]118
53[ 0, 0, 0, 0, 0, 0, 0, 1, 1 ]1288
49[ 0, 0, 0, 0, 0, 0, 1, 0, 0 ]1672
37[ 0, 0, 0, 0, 0, 0, 0, 0, 2 ]118
35[ 0, 0, 0, 0, 0, 0, 0, 1, 0 ]1144
19[ 0, 0, 0, 0, 0, 0, 0, 0, 1 ]918
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0 ]91

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 1, 1 ]
Characteristic: 2
Dimension: 1920

Level   dominant weight   weight multiplicity   length of W-orbit 
53[ 0, 0, 0, 0, 0, 0, 0, 1, 1 ]1288
49[ 0, 0, 0, 0, 0, 0, 1, 0, 0 ]2672
19[ 0, 0, 0, 0, 0, 0, 0, 0, 1 ]1618

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 1, 1 ]
Characteristic: not 2,3
Dimension: 2261

Level   dominant weight   weight multiplicity   length of W-orbit 
53[ 0, 0, 0, 0, 0, 0, 0, 1, 1 ]1288
49[ 0, 0, 0, 0, 0, 0, 1, 0, 0 ]2672
37[ 0, 0, 0, 0, 0, 0, 0, 0, 2 ]118
35[ 0, 0, 0, 0, 0, 0, 0, 1, 0 ]2144
19[ 0, 0, 0, 0, 0, 0, 0, 0, 1 ]1718
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0 ]171

Highest weight: [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ]
Characteristic: 2
Dimension: 2906

Level   dominant weight   weight multiplicity   length of W-orbit 
61[ 0, 0, 0, 0, 0, 1, 0, 0, 0 ]12016
35[ 0, 0, 0, 0, 0, 0, 0, 1, 0 ]6144
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0 ]261

Highest weight: [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ]
Characteristic: not 2
Dimension: 3876

Level   dominant weight   weight multiplicity   length of W-orbit 
61[ 0, 0, 0, 0, 0, 1, 0, 0, 0 ]12016
49[ 0, 0, 0, 0, 0, 0, 1, 0, 0 ]1672
35[ 0, 0, 0, 0, 0, 0, 0, 1, 0 ]7144
19[ 0, 0, 0, 0, 0, 0, 0, 0, 1 ]818
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0 ]361

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 2, 0 ]
Characteristic: 3
Dimension: 6763

Level   dominant weight   weight multiplicity   length of W-orbit 
69[ 0, 0, 0, 0, 0, 0, 0, 2, 0 ]1144
67[ 0, 0, 0, 0, 0, 0, 1, 0, 1 ]12016
61[ 0, 0, 0, 0, 0, 1, 0, 0, 0 ]12016
53[ 0, 0, 0, 0, 0, 0, 0, 1, 1 ]1288
49[ 0, 0, 0, 0, 0, 0, 1, 0, 0 ]1672
37[ 0, 0, 0, 0, 0, 0, 0, 0, 2 ]818
35[ 0, 0, 0, 0, 0, 0, 0, 1, 0 ]9144
19[ 0, 0, 0, 0, 0, 0, 0, 0, 1 ]818
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0 ]431

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 4 ]
Characteristic: 23
Dimension: 6936

Level   dominant weight   weight multiplicity   length of W-orbit 
73[ 0, 0, 0, 0, 0, 0, 0, 0, 4 ]118
71[ 0, 0, 0, 0, 0, 0, 0, 1, 2 ]1288
69[ 0, 0, 0, 0, 0, 0, 0, 2, 0 ]1144
67[ 0, 0, 0, 0, 0, 0, 1, 0, 1 ]12016
61[ 0, 0, 0, 0, 0, 1, 0, 0, 0 ]12016
55[ 0, 0, 0, 0, 0, 0, 0, 0, 3 ]118
53[ 0, 0, 0, 0, 0, 0, 0, 1, 1 ]1288
49[ 0, 0, 0, 0, 0, 0, 1, 0, 0 ]1672
37[ 0, 0, 0, 0, 0, 0, 0, 0, 2 ]818
35[ 0, 0, 0, 0, 0, 0, 0, 1, 0 ]8144
19[ 0, 0, 0, 0, 0, 0, 0, 0, 1 ]818
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0 ]361

Highest weight: [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ]
Characteristic: 2
Dimension: 6972

Level   dominant weight   weight multiplicity   length of W-orbit 
71[ 0, 0, 0, 0, 1, 0, 0, 0, 0 ]14032
49[ 0, 0, 0, 0, 0, 0, 1, 0, 0 ]4672
19[ 0, 0, 0, 0, 0, 0, 0, 0, 1 ]1418

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 4 ]
Characteristic: 7
Dimension: 7124

Level   dominant weight   weight multiplicity   length of W-orbit 
73[ 0, 0, 0, 0, 0, 0, 0, 0, 4 ]118
71[ 0, 0, 0, 0, 0, 0, 0, 1, 2 ]1288
69[ 0, 0, 0, 0, 0, 0, 0, 2, 0 ]1144
67[ 0, 0, 0, 0, 0, 0, 1, 0, 1 ]12016
61[ 0, 0, 0, 0, 0, 1, 0, 0, 0 ]12016
55[ 0, 0, 0, 0, 0, 0, 0, 0, 3 ]118
53[ 0, 0, 0, 0, 0, 0, 0, 1, 1 ]1288
49[ 0, 0, 0, 0, 0, 0, 1, 0, 0 ]1672
37[ 0, 0, 0, 0, 0, 0, 0, 0, 2 ]918
35[ 0, 0, 0, 0, 0, 0, 0, 1, 0 ]9144
19[ 0, 0, 0, 0, 0, 0, 0, 0, 1 ]918
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0 ]441

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 4 ]
Characteristic: not 2,3,7,23
Dimension: 7125

Level   dominant weight   weight multiplicity   length of W-orbit 
73[ 0, 0, 0, 0, 0, 0, 0, 0, 4 ]118
71[ 0, 0, 0, 0, 0, 0, 0, 1, 2 ]1288
69[ 0, 0, 0, 0, 0, 0, 0, 2, 0 ]1144
67[ 0, 0, 0, 0, 0, 0, 1, 0, 1 ]12016
61[ 0, 0, 0, 0, 0, 1, 0, 0, 0 ]12016
55[ 0, 0, 0, 0, 0, 0, 0, 0, 3 ]118
53[ 0, 0, 0, 0, 0, 0, 0, 1, 1 ]1288
49[ 0, 0, 0, 0, 0, 0, 1, 0, 0 ]1672
37[ 0, 0, 0, 0, 0, 0, 0, 0, 2 ]918
35[ 0, 0, 0, 0, 0, 0, 0, 1, 0 ]9144
19[ 0, 0, 0, 0, 0, 0, 0, 0, 1 ]918
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0 ]451