[Overview]

Weight Multiplicities

Groups of type B10, degree bound 10000

Diagram:

1 < 2 - .. - 10

Overview

DimensionHighest weightCharacteristic
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]all
20[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]2
21[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]not 2
188[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]2
210[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]not 2
229[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]3
229[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]7
230[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]not 2, 3, 7
1024[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]all
1120[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]2
1330[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]not 2
1729[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 3 ]23
1729[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]3
1750[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 3 ]not 2, 3, 23
2640[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]2
3038[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]5
3059[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]not 2, 3, 5
4466[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ]2
5985[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ]not 2
9954[ 0, 0, 0, 0, 0, 0, 0, 0, 2, 0 ]3

The characters

Highest weight: [ 0, 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, 0 ]11

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]
Characteristic: 2
Dimension: 20

Level   dominant weight   weight multiplicity   length of W-orbit 
21[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]120

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]
Characteristic: not 2
Dimension: 21

Level   dominant weight   weight multiplicity   length of W-orbit 
21[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]120
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]11

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]
Characteristic: 2
Dimension: 188

Level   dominant weight   weight multiplicity   length of W-orbit 
39[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]1180
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]81

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]
Characteristic: not 2
Dimension: 210

Level   dominant weight   weight multiplicity   length of W-orbit 
39[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]1180
21[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]120
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]101

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]
Characteristic: 3
Dimension: 229

Level   dominant weight   weight multiplicity   length of W-orbit 
41[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]120
39[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]1180
21[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]120
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]91

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]
Characteristic: 7
Dimension: 229

Level   dominant weight   weight multiplicity   length of W-orbit 
41[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]120
39[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]1180
21[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]120
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]91

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]
Characteristic: not 2,3,7
Dimension: 230

Level   dominant weight   weight multiplicity   length of W-orbit 
41[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]120
39[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]1180
21[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]120
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]101

Highest weight: [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
Characteristic: all
Dimension: 1024

Level   dominant weight   weight multiplicity   length of W-orbit 
56[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]11024

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]
Characteristic: 2
Dimension: 1120

Level   dominant weight   weight multiplicity   length of W-orbit 
55[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]1960
21[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]820

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]
Characteristic: not 2
Dimension: 1330

Level   dominant weight   weight multiplicity   length of W-orbit 
55[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]1960
39[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]1180
21[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]920
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]101

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 3 ]
Characteristic: 23
Dimension: 1729

Level   dominant weight   weight multiplicity   length of W-orbit 
61[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 3 ]120
59[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]1360
55[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]1960
41[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]120
39[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]1180
21[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]920
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]91

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]
Characteristic: 3
Dimension: 1729

Level   dominant weight   weight multiplicity   length of W-orbit 
59[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]1360
55[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]1960
41[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]120
39[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]1180
21[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]1020
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]91

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 3 ]
Characteristic: not 2,3,23
Dimension: 1750

Level   dominant weight   weight multiplicity   length of W-orbit 
61[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 3 ]120
59[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]1360
55[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]1960
41[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]120
39[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]1180
21[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]1020
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]101

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]
Characteristic: 2
Dimension: 2640

Level   dominant weight   weight multiplicity   length of W-orbit 
59[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]1360
55[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]2960
21[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]1820

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]
Characteristic: 5
Dimension: 3038

Level   dominant weight   weight multiplicity   length of W-orbit 
59[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]1360
55[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]2960
41[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]120
39[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]2180
21[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]1820
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]181

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]
Characteristic: not 2,3,5
Dimension: 3059

Level   dominant weight   weight multiplicity   length of W-orbit 
59[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]1360
55[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]2960
41[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]120
39[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]2180
21[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]1920
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]191

Highest weight: [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ]
Characteristic: 2
Dimension: 4466

Level   dominant weight   weight multiplicity   length of W-orbit 
69[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ]13360
39[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]6180
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]261

Highest weight: [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ]
Characteristic: not 2
Dimension: 5985

Level   dominant weight   weight multiplicity   length of W-orbit 
69[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ]13360
55[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]1960
39[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]8180
21[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]920
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]451

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 2, 0 ]
Characteristic: 3
Dimension: 9954

Level   dominant weight   weight multiplicity   length of W-orbit 
77[ 0, 0, 0, 0, 0, 0, 0, 0, 2, 0 ]1180
75[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1 ]12880
69[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ]13360
59[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]1360
55[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]1960
41[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]920
39[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]10180
21[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]920
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]541