[Overview]

Weight Multiplicities

Groups of type D9, degree bound 15000

Diagram:

 1
  \
   3 - 4 - .. - 9
  /
 2

Overview

DimensionHighest weightCharacteristic
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0 ]all
18[ 0, 0, 0, 0, 0, 0, 0, 0, 1 ]all
152[ 0, 0, 0, 0, 0, 0, 0, 1, 0 ]2
153[ 0, 0, 0, 0, 0, 0, 0, 1, 0 ]not 2
169[ 0, 0, 0, 0, 0, 0, 0, 0, 2 ]3
170[ 0, 0, 0, 0, 0, 0, 0, 0, 2 ]not 2, 3
256[ 0, 1, 0, 0, 0, 0, 0, 0, 0 ]all
256[ 1, 0, 0, 0, 0, 0, 0, 0, 0 ]all
780[ 0, 0, 0, 0, 0, 0, 1, 0, 0 ]2
816[ 0, 0, 0, 0, 0, 0, 1, 0, 0 ]not 2
1104[ 0, 0, 0, 0, 0, 0, 0, 0, 3 ]5
1104[ 0, 0, 0, 0, 0, 0, 0, 1, 1 ]3
1122[ 0, 0, 0, 0, 0, 0, 0, 0, 3 ]not 2, 3, 5
1902[ 0, 0, 0, 0, 0, 0, 0, 1, 1 ]17
1920[ 0, 0, 0, 0, 0, 0, 0, 1, 1 ]not 3, 17
2906[ 0, 0, 0, 0, 0, 1, 0, 0, 0 ]2
3060[ 0, 0, 0, 0, 0, 1, 0, 0, 0 ]not 2
4096[ 0, 1, 0, 0, 0, 0, 0, 0, 1 ]3
4096[ 1, 0, 0, 0, 0, 0, 0, 0, 1 ]3
4352[ 0, 1, 0, 0, 0, 0, 0, 0, 1 ]not 3
4352[ 1, 0, 0, 0, 0, 0, 0, 0, 1 ]not 3
5490[ 0, 0, 0, 0, 0, 0, 0, 2, 0 ]3
5644[ 0, 0, 0, 0, 0, 0, 0, 0, 4 ]11
5813[ 0, 0, 0, 0, 0, 0, 0, 0, 4 ]5
5814[ 0, 0, 0, 0, 0, 0, 0, 0, 4 ]not 2, 3, 5, 11
6972[ 0, 0, 0, 0, 1, 0, 0, 0, 0 ]2
8226[ 0, 0, 0, 0, 0, 0, 1, 0, 1 ]2
8549[ 0, 0, 0, 0, 0, 0, 0, 2, 0 ]17
8550[ 0, 0, 0, 0, 0, 0, 0, 2, 0 ]not 2, 3, 17
8568[ 0, 0, 0, 0, 1, 0, 0, 0, 0 ]not 2
11475[ 0, 0, 0, 0, 0, 0, 1, 0, 1 ]not 2
14043[ 0, 0, 0, 0, 0, 0, 0, 1, 2 ]3
14059[ 0, 0, 0, 0, 0, 0, 0, 1, 2 ]5
14212[ 0, 0, 0, 0, 0, 0, 0, 1, 2 ]not 2, 3, 5

The characters


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: all
Dimension: 18

Level   dominant weight   weight multiplicity   length of W-orbit 
17[ 0, 0, 0, 0, 0, 0, 0, 0, 1 ]118

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

Level   dominant weight   weight multiplicity   length of W-orbit 
31[ 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: 153

Level   dominant weight   weight multiplicity   length of W-orbit 
31[ 0, 0, 0, 0, 0, 0, 0, 1, 0 ]1144
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0 ]91

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 2 ]
Characteristic: 3
Dimension: 169

Level   dominant weight   weight multiplicity   length of W-orbit 
33[ 0, 0, 0, 0, 0, 0, 0, 0, 2 ]118
31[ 0, 0, 0, 0, 0, 0, 0, 1, 0 ]1144
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0 ]71

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 2 ]
Characteristic: not 2,3
Dimension: 170

Level   dominant weight   weight multiplicity   length of W-orbit 
33[ 0, 0, 0, 0, 0, 0, 0, 0, 2 ]118
31[ 0, 0, 0, 0, 0, 0, 0, 1, 0 ]1144
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0 ]81

Highest weight: [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ]
Characteristic: all
Dimension: 256

Level   dominant weight   weight multiplicity   length of W-orbit 
37[ 0, 1, 0, 0, 0, 0, 0, 0, 0 ]1256

Highest weight: [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ]
Characteristic: all
Dimension: 256

Level   dominant weight   weight multiplicity   length of W-orbit 
37[ 1, 0, 0, 0, 0, 0, 0, 0, 0 ]1256

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

Level   dominant weight   weight multiplicity   length of W-orbit 
43[ 0, 0, 0, 0, 0, 0, 1, 0, 0 ]1672
17[ 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: 816

Level   dominant weight   weight multiplicity   length of W-orbit 
43[ 0, 0, 0, 0, 0, 0, 1, 0, 0 ]1672
17[ 0, 0, 0, 0, 0, 0, 0, 0, 1 ]818

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 3 ]
Characteristic: 5
Dimension: 1104

Level   dominant weight   weight multiplicity   length of W-orbit 
49[ 0, 0, 0, 0, 0, 0, 0, 0, 3 ]118
47[ 0, 0, 0, 0, 0, 0, 0, 1, 1 ]1288
43[ 0, 0, 0, 0, 0, 0, 1, 0, 0 ]1672
17[ 0, 0, 0, 0, 0, 0, 0, 0, 1 ]718

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 1, 1 ]
Characteristic: 3
Dimension: 1104

Level   dominant weight   weight multiplicity   length of W-orbit 
47[ 0, 0, 0, 0, 0, 0, 0, 1, 1 ]1288
43[ 0, 0, 0, 0, 0, 0, 1, 0, 0 ]1672
17[ 0, 0, 0, 0, 0, 0, 0, 0, 1 ]818

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 3 ]
Characteristic: not 2,3,5
Dimension: 1122

Level   dominant weight   weight multiplicity   length of W-orbit 
49[ 0, 0, 0, 0, 0, 0, 0, 0, 3 ]118
47[ 0, 0, 0, 0, 0, 0, 0, 1, 1 ]1288
43[ 0, 0, 0, 0, 0, 0, 1, 0, 0 ]1672
17[ 0, 0, 0, 0, 0, 0, 0, 0, 1 ]818

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 1, 1 ]
Characteristic: 17
Dimension: 1902

Level   dominant weight   weight multiplicity   length of W-orbit 
47[ 0, 0, 0, 0, 0, 0, 0, 1, 1 ]1288
43[ 0, 0, 0, 0, 0, 0, 1, 0, 0 ]2672
17[ 0, 0, 0, 0, 0, 0, 0, 0, 1 ]1518

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 1, 1 ]
Characteristic: not 3,17
Dimension: 1920

Level   dominant weight   weight multiplicity   length of W-orbit 
47[ 0, 0, 0, 0, 0, 0, 0, 1, 1 ]1288
43[ 0, 0, 0, 0, 0, 0, 1, 0, 0 ]2672
17[ 0, 0, 0, 0, 0, 0, 0, 0, 1 ]1618

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

Level   dominant weight   weight multiplicity   length of W-orbit 
53[ 0, 0, 0, 0, 0, 1, 0, 0, 0 ]12016
31[ 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: 3060

Level   dominant weight   weight multiplicity   length of W-orbit 
53[ 0, 0, 0, 0, 0, 1, 0, 0, 0 ]12016
31[ 0, 0, 0, 0, 0, 0, 0, 1, 0 ]7144
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0 ]361

Highest weight: [ 0, 1, 0, 0, 0, 0, 0, 0, 1 ]
Characteristic: 3
Dimension: 4096

Level   dominant weight   weight multiplicity   length of W-orbit 
53[ 0, 1, 0, 0, 0, 0, 0, 0, 1 ]12304
37[ 1, 0, 0, 0, 0, 0, 0, 0, 0 ]7256

Highest weight: [ 1, 0, 0, 0, 0, 0, 0, 0, 1 ]
Characteristic: 3
Dimension: 4096

Level   dominant weight   weight multiplicity   length of W-orbit 
53[ 1, 0, 0, 0, 0, 0, 0, 0, 1 ]12304
37[ 0, 1, 0, 0, 0, 0, 0, 0, 0 ]7256

Highest weight: [ 0, 1, 0, 0, 0, 0, 0, 0, 1 ]
Characteristic: not 3
Dimension: 4352

Level   dominant weight   weight multiplicity   length of W-orbit 
53[ 0, 1, 0, 0, 0, 0, 0, 0, 1 ]12304
37[ 1, 0, 0, 0, 0, 0, 0, 0, 0 ]8256

Highest weight: [ 1, 0, 0, 0, 0, 0, 0, 0, 1 ]
Characteristic: not 3
Dimension: 4352

Level   dominant weight   weight multiplicity   length of W-orbit 
53[ 1, 0, 0, 0, 0, 0, 0, 0, 1 ]12304
37[ 0, 1, 0, 0, 0, 0, 0, 0, 0 ]8256

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 2, 0 ]
Characteristic: 3
Dimension: 5490

Level   dominant weight   weight multiplicity   length of W-orbit 
61[ 0, 0, 0, 0, 0, 0, 0, 2, 0 ]1144
59[ 0, 0, 0, 0, 0, 0, 1, 0, 1 ]12016
53[ 0, 0, 0, 0, 0, 1, 0, 0, 0 ]12016
33[ 0, 0, 0, 0, 0, 0, 0, 0, 2 ]718
31[ 0, 0, 0, 0, 0, 0, 0, 1, 0 ]8144
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0 ]361

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 4 ]
Characteristic: 11
Dimension: 5644

Level   dominant weight   weight multiplicity   length of W-orbit 
65[ 0, 0, 0, 0, 0, 0, 0, 0, 4 ]118
63[ 0, 0, 0, 0, 0, 0, 0, 1, 2 ]1288
61[ 0, 0, 0, 0, 0, 0, 0, 2, 0 ]1144
59[ 0, 0, 0, 0, 0, 0, 1, 0, 1 ]12016
53[ 0, 0, 0, 0, 0, 1, 0, 0, 0 ]12016
33[ 0, 0, 0, 0, 0, 0, 0, 0, 2 ]718
31[ 0, 0, 0, 0, 0, 0, 0, 1, 0 ]7144
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0 ]281

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 4 ]
Characteristic: 5
Dimension: 5813

Level   dominant weight   weight multiplicity   length of W-orbit 
65[ 0, 0, 0, 0, 0, 0, 0, 0, 4 ]118
63[ 0, 0, 0, 0, 0, 0, 0, 1, 2 ]1288
61[ 0, 0, 0, 0, 0, 0, 0, 2, 0 ]1144
59[ 0, 0, 0, 0, 0, 0, 1, 0, 1 ]12016
53[ 0, 0, 0, 0, 0, 1, 0, 0, 0 ]12016
33[ 0, 0, 0, 0, 0, 0, 0, 0, 2 ]818
31[ 0, 0, 0, 0, 0, 0, 0, 1, 0 ]8144
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0 ]351

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 4 ]
Characteristic: not 2,3,5,11
Dimension: 5814

Level   dominant weight   weight multiplicity   length of W-orbit 
65[ 0, 0, 0, 0, 0, 0, 0, 0, 4 ]118
63[ 0, 0, 0, 0, 0, 0, 0, 1, 2 ]1288
61[ 0, 0, 0, 0, 0, 0, 0, 2, 0 ]1144
59[ 0, 0, 0, 0, 0, 0, 1, 0, 1 ]12016
53[ 0, 0, 0, 0, 0, 1, 0, 0, 0 ]12016
33[ 0, 0, 0, 0, 0, 0, 0, 0, 2 ]818
31[ 0, 0, 0, 0, 0, 0, 0, 1, 0 ]8144
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 
61[ 0, 0, 0, 0, 1, 0, 0, 0, 0 ]14032
43[ 0, 0, 0, 0, 0, 0, 1, 0, 0 ]4672
17[ 0, 0, 0, 0, 0, 0, 0, 0, 1 ]1418

Highest weight: [ 0, 0, 0, 0, 0, 0, 1, 0, 1 ]
Characteristic: 2
Dimension: 8226

Level   dominant weight   weight multiplicity   length of W-orbit 
59[ 0, 0, 0, 0, 0, 0, 1, 0, 1 ]12016
53[ 0, 0, 0, 0, 0, 1, 0, 0, 0 ]22016
33[ 0, 0, 0, 0, 0, 0, 0, 0, 2 ]618
31[ 0, 0, 0, 0, 0, 0, 0, 1, 0 ]14144
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0 ]541

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 2, 0 ]
Characteristic: 17
Dimension: 8549

Level   dominant weight   weight multiplicity   length of W-orbit 
61[ 0, 0, 0, 0, 0, 0, 0, 2, 0 ]1144
59[ 0, 0, 0, 0, 0, 0, 1, 0, 1 ]12016
53[ 0, 0, 0, 0, 0, 1, 0, 0, 0 ]22016
33[ 0, 0, 0, 0, 0, 0, 0, 0, 2 ]718
31[ 0, 0, 0, 0, 0, 0, 0, 1, 0 ]15144
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0 ]711

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 2, 0 ]
Characteristic: not 2,3,17
Dimension: 8550

Level   dominant weight   weight multiplicity   length of W-orbit 
61[ 0, 0, 0, 0, 0, 0, 0, 2, 0 ]1144
59[ 0, 0, 0, 0, 0, 0, 1, 0, 1 ]12016
53[ 0, 0, 0, 0, 0, 1, 0, 0, 0 ]22016
33[ 0, 0, 0, 0, 0, 0, 0, 0, 2 ]718
31[ 0, 0, 0, 0, 0, 0, 0, 1, 0 ]15144
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0 ]721

Highest weight: [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ]
Characteristic: not 2
Dimension: 8568

Level   dominant weight   weight multiplicity   length of W-orbit 
61[ 0, 0, 0, 0, 1, 0, 0, 0, 0 ]14032
43[ 0, 0, 0, 0, 0, 0, 1, 0, 0 ]6672
17[ 0, 0, 0, 0, 0, 0, 0, 0, 1 ]2818

Highest weight: [ 0, 0, 0, 0, 0, 0, 1, 0, 1 ]
Characteristic: not 2
Dimension: 11475

Level   dominant weight   weight multiplicity   length of W-orbit 
59[ 0, 0, 0, 0, 0, 0, 1, 0, 1 ]12016
53[ 0, 0, 0, 0, 0, 1, 0, 0, 0 ]32016
33[ 0, 0, 0, 0, 0, 0, 0, 0, 2 ]818
31[ 0, 0, 0, 0, 0, 0, 0, 1, 0 ]22144
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0 ]991

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 1, 2 ]
Characteristic: 3
Dimension: 14043

Level   dominant weight   weight multiplicity   length of W-orbit 
63[ 0, 0, 0, 0, 0, 0, 0, 1, 2 ]1288
61[ 0, 0, 0, 0, 0, 0, 0, 2, 0 ]1144
59[ 0, 0, 0, 0, 0, 0, 1, 0, 1 ]22016
53[ 0, 0, 0, 0, 0, 1, 0, 0, 0 ]32016
33[ 0, 0, 0, 0, 0, 0, 0, 0, 2 ]1518
31[ 0, 0, 0, 0, 0, 0, 0, 1, 0 ]22144
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0 ]931

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 1, 2 ]
Characteristic: 5
Dimension: 14059

Level   dominant weight   weight multiplicity   length of W-orbit 
63[ 0, 0, 0, 0, 0, 0, 0, 1, 2 ]1288
61[ 0, 0, 0, 0, 0, 0, 0, 2, 0 ]1144
59[ 0, 0, 0, 0, 0, 0, 1, 0, 1 ]22016
53[ 0, 0, 0, 0, 0, 1, 0, 0, 0 ]32016
33[ 0, 0, 0, 0, 0, 0, 0, 0, 2 ]1618
31[ 0, 0, 0, 0, 0, 0, 0, 1, 0 ]22144
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0 ]911

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 1, 2 ]
Characteristic: not 2,3,5
Dimension: 14212

Level   dominant weight   weight multiplicity   length of W-orbit 
63[ 0, 0, 0, 0, 0, 0, 0, 1, 2 ]1288
61[ 0, 0, 0, 0, 0, 0, 0, 2, 0 ]1144
59[ 0, 0, 0, 0, 0, 0, 1, 0, 1 ]22016
53[ 0, 0, 0, 0, 0, 1, 0, 0, 0 ]32016
33[ 0, 0, 0, 0, 0, 0, 0, 0, 2 ]1618
31[ 0, 0, 0, 0, 0, 0, 0, 1, 0 ]23144
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0 ]1001