[Overview]

Weight Multiplicities

Groups of type D11, degree bound 20000

Diagram:

 1
  \
   3 - 4 - .. - 11
  /
 2

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 ]all
230[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]2
231[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]not 2
251[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]11
252[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]not 2, 11
1024[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]all
1024[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]all
1496[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]2
1540[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]not 2
1958[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]3
2002[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3 ]not 2, 3
3498[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]7
3520[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]not 3, 7
7084[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ]2
7315[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ]not 2
11912[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0 ]3
12145[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4 ]13
12397[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4 ]not 2, 3, 13
18744[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1 ]2
18976[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0 ]5
19227[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0 ]7
19228[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0 ]not 2, 3, 5, 7

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: all
Dimension: 22

Level   dominant weight   weight multiplicity   length of W-orbit 
21[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]122

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 
39[ 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: 231

Level   dominant weight   weight multiplicity   length of W-orbit 
39[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]1220
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: 11
Dimension: 251

Level   dominant weight   weight multiplicity   length of W-orbit 
41[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]122
39[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]1220
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]91

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]
Characteristic: not 2,11
Dimension: 252

Level   dominant weight   weight multiplicity   length of W-orbit 
41[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]122
39[ 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
Characteristic: all
Dimension: 1024

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

Highest weight: [ 1, 0, 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, 0 ]11024

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 
55[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]11320
21[ 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: 1540

Level   dominant weight   weight multiplicity   length of W-orbit 
55[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]11320
21[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]1022

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]
Characteristic: 3
Dimension: 1958

Level   dominant weight   weight multiplicity   length of W-orbit 
59[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]1440
55[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]11320
21[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]922

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3 ]
Characteristic: not 2,3
Dimension: 2002

Level   dominant weight   weight multiplicity   length of W-orbit 
61[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3 ]122
59[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]1440
55[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]11320
21[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]1022

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]
Characteristic: 7
Dimension: 3498

Level   dominant weight   weight multiplicity   length of W-orbit 
59[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]1440
55[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]21320
21[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]1922

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]
Characteristic: not 3,7
Dimension: 3520

Level   dominant weight   weight multiplicity   length of W-orbit 
59[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]1440
55[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]21320
21[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]2022

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 
69[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ]15280
39[ 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: 7315

Level   dominant weight   weight multiplicity   length of W-orbit 
69[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ]15280
39[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]9220
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]551

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0 ]
Characteristic: 3
Dimension: 11912

Level   dominant weight   weight multiplicity   length of W-orbit 
77[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0 ]1220
75[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1 ]13960
69[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ]15280
41[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]922
39[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]10220
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]541

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4 ]
Characteristic: 13
Dimension: 12145

Level   dominant weight   weight multiplicity   length of W-orbit 
81[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4 ]122
79[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2 ]1440
77[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0 ]1220
75[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1 ]13960
69[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ]15280
41[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]922
39[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]9220
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]451

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4 ]
Characteristic: not 2,3,13
Dimension: 12397

Level   dominant weight   weight multiplicity   length of W-orbit 
81[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4 ]122
79[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2 ]1440
77[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0 ]1220
75[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1 ]13960
69[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ]15280
41[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]1022
39[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]10220
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]551

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1 ]
Characteristic: 2
Dimension: 18744

Level   dominant weight   weight multiplicity   length of W-orbit 
75[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1 ]13960
69[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ]25280
41[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]822
39[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]18220
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]881

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0 ]
Characteristic: 5
Dimension: 18976

Level   dominant weight   weight multiplicity   length of W-orbit 
77[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0 ]1220
75[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1 ]13960
69[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ]25280
41[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]822
39[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]18220
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]1001

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0 ]
Characteristic: 7
Dimension: 19227

Level   dominant weight   weight multiplicity   length of W-orbit 
77[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0 ]1220
75[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1 ]13960
69[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ]25280
41[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]922
39[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]19220
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]1091

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0 ]
Characteristic: not 2,3,5,7
Dimension: 19228

Level   dominant weight   weight multiplicity   length of W-orbit 
77[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0 ]1220
75[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1 ]13960
69[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ]25280
41[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]922
39[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]19220
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]1101