[Overview]

Weight Multiplicities

Groups of type B11, degree bound 12000

Diagram:

1 < 2 - .. - 11

Overview

DimensionHighest weightCharacteristic
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]all
22[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]2
23[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]not 2
230[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]2
253[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]not 2
274[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]23
275[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]not 2, 23
1496[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]2
1771[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]not 2
2048[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]all
2254[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3 ]5
2254[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]3
2277[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3 ]not 2, 3, 5
3520[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]2
4002[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]11
4025[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]not 2, 3, 11
7084[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ]2
8855[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ]not 2

The characters


Highest weight: [ 0, 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, 0 ]11

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]
Characteristic: 2
Dimension: 22

Level   dominant weight   weight multiplicity   length of W-orbit 
23[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]122

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]
Characteristic: not 2
Dimension: 23

Level   dominant weight   weight multiplicity   length of W-orbit 
23[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]122
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]11

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]
Characteristic: 2
Dimension: 230

Level   dominant weight   weight multiplicity   length of W-orbit 
43[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]1220
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]101

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]
Characteristic: not 2
Dimension: 253

Level   dominant weight   weight multiplicity   length of W-orbit 
43[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]1220
23[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]122
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]111

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]
Characteristic: 23
Dimension: 274

Level   dominant weight   weight multiplicity   length of W-orbit 
45[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]122
43[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]1220
23[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]122
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]101

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]
Characteristic: not 2,23
Dimension: 275

Level   dominant weight   weight multiplicity   length of W-orbit 
45[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]122
43[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]1220
23[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]122
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]111

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]
Characteristic: 2
Dimension: 1496

Level   dominant weight   weight multiplicity   length of W-orbit 
61[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]11320
23[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]822

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]
Characteristic: not 2
Dimension: 1771

Level   dominant weight   weight multiplicity   length of W-orbit 
61[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]11320
43[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]1220
23[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]1022
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]111

Highest weight: [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
Characteristic: all
Dimension: 2048

Level   dominant weight   weight multiplicity   length of W-orbit 
67[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]12048

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3 ]
Characteristic: 5
Dimension: 2254

Level   dominant weight   weight multiplicity   length of W-orbit 
67[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3 ]122
65[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]1440
61[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]11320
45[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]122
43[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]1220
23[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]1022
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]101

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]
Characteristic: 3
Dimension: 2254

Level   dominant weight   weight multiplicity   length of W-orbit 
65[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]1440
61[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]11320
45[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]122
43[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]1220
23[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]1122
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]101

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3 ]
Characteristic: not 2,3,5
Dimension: 2277

Level   dominant weight   weight multiplicity   length of W-orbit 
67[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3 ]122
65[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]1440
61[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]11320
45[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]122
43[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]1220
23[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]1122
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]111

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]
Characteristic: 2
Dimension: 3520

Level   dominant weight   weight multiplicity   length of W-orbit 
65[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]1440
61[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]21320
23[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]2022

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]
Characteristic: 11
Dimension: 4002

Level   dominant weight   weight multiplicity   length of W-orbit 
65[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]1440
61[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]21320
45[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]122
43[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]2220
23[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]2022
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]201

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]
Characteristic: not 2,3,11
Dimension: 4025

Level   dominant weight   weight multiplicity   length of W-orbit 
65[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]1440
61[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]21320
45[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]122
43[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]2220
23[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]2122
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]211

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ]
Characteristic: 2
Dimension: 7084

Level   dominant weight   weight multiplicity   length of W-orbit 
77[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ]15280
43[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]8220
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]441

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ]
Characteristic: not 2
Dimension: 8855

Level   dominant weight   weight multiplicity   length of W-orbit 
77[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ]15280
61[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]11320
43[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]9220
23[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]1022
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]551