[Overview]

Weight Multiplicities

Groups of type D10, degree bound 18000

Diagram:

 1
  \
   3 - 4 - .. - 10
  /
 2

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 ]all
188[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]2
190[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]not 2
208[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]5
209[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]not 2, 5
512[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ]all
512[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]all
1120[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]2
1140[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]not 2
1500[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 3 ]11
1500[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]3
1520[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 3 ]not 2, 3, 11
2620[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]19
2640[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]not 3, 19
4466[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ]2
4845[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ]not 2
8036[ 0, 0, 0, 0, 0, 0, 0, 0, 2, 0 ]3
8644[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 4 ]11
8645[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 4 ]not 2, 3, 11
9216[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1 ]2
9216[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1 ]5
9216[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]2
9216[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]5
9728[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1 ]not 2, 5
9728[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]not 2, 5
12712[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1 ]2
13089[ 0, 0, 0, 0, 0, 0, 0, 0, 2, 0 ]19
13090[ 0, 0, 0, 0, 0, 0, 0, 0, 2, 0 ]not 2, 3, 19
14344[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ]2
15504[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ]not 2
17575[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1 ]3
17765[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1 ]not 2, 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: all
Dimension: 20

Level   dominant weight   weight multiplicity   length of W-orbit 
19[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]120

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 
35[ 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: 190

Level   dominant weight   weight multiplicity   length of W-orbit 
35[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]1180
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: 5
Dimension: 208

Level   dominant weight   weight multiplicity   length of W-orbit 
37[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]120
35[ 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, 0, 2 ]
Characteristic: not 2,5
Dimension: 209

Level   dominant weight   weight multiplicity   length of W-orbit 
37[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]120
35[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]1180
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]91

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

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

Highest weight: [ 1, 0, 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, 0 ]1512

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 
49[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]1960
19[ 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: 1140

Level   dominant weight   weight multiplicity   length of W-orbit 
49[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]1960
19[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]920

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 3 ]
Characteristic: 11
Dimension: 1500

Level   dominant weight   weight multiplicity   length of W-orbit 
55[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 3 ]120
53[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]1360
49[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]1960
19[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]820

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]
Characteristic: 3
Dimension: 1500

Level   dominant weight   weight multiplicity   length of W-orbit 
53[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]1360
49[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]1960
19[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]920

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 3 ]
Characteristic: not 2,3,11
Dimension: 1520

Level   dominant weight   weight multiplicity   length of W-orbit 
55[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 3 ]120
53[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]1360
49[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]1960
19[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]920

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]
Characteristic: 19
Dimension: 2620

Level   dominant weight   weight multiplicity   length of W-orbit 
53[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]1360
49[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]2960
19[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]1720

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]
Characteristic: not 3,19
Dimension: 2640

Level   dominant weight   weight multiplicity   length of W-orbit 
53[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]1360
49[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]2960
19[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]1820

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 
61[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ]13360
35[ 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: 4845

Level   dominant weight   weight multiplicity   length of W-orbit 
61[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ]13360
35[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]8180
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: 8036

Level   dominant weight   weight multiplicity   length of W-orbit 
69[ 0, 0, 0, 0, 0, 0, 0, 0, 2, 0 ]1180
67[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1 ]12880
61[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ]13360
37[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]720
35[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]8180
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]361

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 4 ]
Characteristic: 11
Dimension: 8644

Level   dominant weight   weight multiplicity   length of W-orbit 
73[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 4 ]120
71[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 2 ]1360
69[ 0, 0, 0, 0, 0, 0, 0, 0, 2, 0 ]1180
67[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1 ]12880
61[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ]13360
37[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]920
35[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]9180
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]441

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 4 ]
Characteristic: not 2,3,11
Dimension: 8645

Level   dominant weight   weight multiplicity   length of W-orbit 
73[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 4 ]120
71[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 2 ]1360
69[ 0, 0, 0, 0, 0, 0, 0, 0, 2, 0 ]1180
67[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1 ]12880
61[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ]13360
37[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]920
35[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]9180
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]451

Highest weight: [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1 ]
Characteristic: 2
Dimension: 9216

Level   dominant weight   weight multiplicity   length of W-orbit 
64[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1 ]15120
46[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]8512

Highest weight: [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1 ]
Characteristic: 5
Dimension: 9216

Level   dominant weight   weight multiplicity   length of W-orbit 
64[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1 ]15120
46[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]8512

Highest weight: [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]
Characteristic: 2
Dimension: 9216

Level   dominant weight   weight multiplicity   length of W-orbit 
64[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]15120
46[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ]8512

Highest weight: [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]
Characteristic: 5
Dimension: 9216

Level   dominant weight   weight multiplicity   length of W-orbit 
64[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]15120
46[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ]8512

Highest weight: [ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1 ]
Characteristic: not 2,5
Dimension: 9728

Level   dominant weight   weight multiplicity   length of W-orbit 
64[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 1 ]15120
46[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]9512

Highest weight: [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]
Characteristic: not 2,5
Dimension: 9728

Level   dominant weight   weight multiplicity   length of W-orbit 
64[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]15120
46[ 0, 1, 0, 0, 0, 0, 0, 0, 0, 0 ]9512

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1 ]
Characteristic: 2
Dimension: 12712

Level   dominant weight   weight multiplicity   length of W-orbit 
67[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1 ]12880
61[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ]23360
37[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]820
35[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]16180
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]721

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 2, 0 ]
Characteristic: 19
Dimension: 13089

Level   dominant weight   weight multiplicity   length of W-orbit 
69[ 0, 0, 0, 0, 0, 0, 0, 0, 2, 0 ]1180
67[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1 ]12880
61[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ]23360
37[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]820
35[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]17180
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]891

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 2, 0 ]
Characteristic: not 2,3,19
Dimension: 13090

Level   dominant weight   weight multiplicity   length of W-orbit 
69[ 0, 0, 0, 0, 0, 0, 0, 0, 2, 0 ]1180
67[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1 ]12880
61[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ]23360
37[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]820
35[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]17180
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]901

Highest weight: [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ]
Characteristic: 2
Dimension: 14344

Level   dominant weight   weight multiplicity   length of W-orbit 
71[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ]18064
49[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]6960
19[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]2620

Highest weight: [ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ]
Characteristic: not 2
Dimension: 15504

Level   dominant weight   weight multiplicity   length of W-orbit 
71[ 0, 0, 0, 0, 0, 1, 0, 0, 0, 0 ]18064
49[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]7960
19[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]3620

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1 ]
Characteristic: 3
Dimension: 17575

Level   dominant weight   weight multiplicity   length of W-orbit 
67[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1 ]12880
61[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ]33360
37[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]920
35[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]24180
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]1151

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1 ]
Characteristic: not 2,3
Dimension: 17765

Level   dominant weight   weight multiplicity   length of W-orbit 
67[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1 ]12880
61[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ]33360
37[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]920
35[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]25180
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]1251