[Overview]

Weight Multiplicities

Groups of type B8, degree bound 7000

Diagram:

1 < 2 - .. - 8

Highest weight: [ 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 ]11

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 1 ]
Characteristic: 2
Dimension: 16

Level   dominant weight   weight multiplicity   length of W-orbit 
17[ 0, 0, 0, 0, 0, 0, 0, 1 ]116

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 1 ]
Characteristic: not 2
Dimension: 17

Level   dominant weight   weight multiplicity   length of W-orbit 
17[ 0, 0, 0, 0, 0, 0, 0, 1 ]116
1[ 0, 0, 0, 0, 0, 0, 0, 0 ]11

Highest weight: [ 0, 0, 0, 0, 0, 0, 1, 0 ]
Characteristic: 2
Dimension: 118

Level   dominant weight   weight multiplicity   length of W-orbit 
31[ 0, 0, 0, 0, 0, 0, 1, 0 ]1112
1[ 0, 0, 0, 0, 0, 0, 0, 0 ]61

Highest weight: [ 0, 0, 0, 0, 0, 0, 1, 0 ]
Characteristic: not 2
Dimension: 136

Level   dominant weight   weight multiplicity   length of W-orbit 
31[ 0, 0, 0, 0, 0, 0, 1, 0 ]1112
17[ 0, 0, 0, 0, 0, 0, 0, 1 ]116
1[ 0, 0, 0, 0, 0, 0, 0, 0 ]81

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 2 ]
Characteristic: 17
Dimension: 151

Level   dominant weight   weight multiplicity   length of W-orbit 
33[ 0, 0, 0, 0, 0, 0, 0, 2 ]116
31[ 0, 0, 0, 0, 0, 0, 1, 0 ]1112
17[ 0, 0, 0, 0, 0, 0, 0, 1 ]116
1[ 0, 0, 0, 0, 0, 0, 0, 0 ]71

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 2 ]
Characteristic: not 2,17
Dimension: 152

Level   dominant weight   weight multiplicity   length of W-orbit 
33[ 0, 0, 0, 0, 0, 0, 0, 2 ]116
31[ 0, 0, 0, 0, 0, 0, 1, 0 ]1112
17[ 0, 0, 0, 0, 0, 0, 0, 1 ]116
1[ 0, 0, 0, 0, 0, 0, 0, 0 ]81

Highest weight: [ 1, 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 ]1256

Highest weight: [ 0, 0, 0, 0, 0, 1, 0, 0 ]
Characteristic: 2
Dimension: 544

Level   dominant weight   weight multiplicity   length of W-orbit 
43[ 0, 0, 0, 0, 0, 1, 0, 0 ]1448
17[ 0, 0, 0, 0, 0, 0, 0, 1 ]616

Highest weight: [ 0, 0, 0, 0, 0, 1, 0, 0 ]
Characteristic: not 2
Dimension: 680

Level   dominant weight   weight multiplicity   length of W-orbit 
43[ 0, 0, 0, 0, 0, 1, 0, 0 ]1448
31[ 0, 0, 0, 0, 0, 0, 1, 0 ]1112
17[ 0, 0, 0, 0, 0, 0, 0, 1 ]716
1[ 0, 0, 0, 0, 0, 0, 0, 0 ]81

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 3 ]
Characteristic: 19
Dimension: 935

Level   dominant weight   weight multiplicity   length of W-orbit 
49[ 0, 0, 0, 0, 0, 0, 0, 3 ]116
47[ 0, 0, 0, 0, 0, 0, 1, 1 ]1224
43[ 0, 0, 0, 0, 0, 1, 0, 0 ]1448
33[ 0, 0, 0, 0, 0, 0, 0, 2 ]116
31[ 0, 0, 0, 0, 0, 0, 1, 0 ]1112
17[ 0, 0, 0, 0, 0, 0, 0, 1 ]716
1[ 0, 0, 0, 0, 0, 0, 0, 0 ]71

Highest weight: [ 0, 0, 0, 0, 0, 0, 1, 1 ]
Characteristic: 3
Dimension: 935

Level   dominant weight   weight multiplicity   length of W-orbit 
47[ 0, 0, 0, 0, 0, 0, 1, 1 ]1224
43[ 0, 0, 0, 0, 0, 1, 0, 0 ]1448
33[ 0, 0, 0, 0, 0, 0, 0, 2 ]116
31[ 0, 0, 0, 0, 0, 0, 1, 0 ]1112
17[ 0, 0, 0, 0, 0, 0, 0, 1 ]816
1[ 0, 0, 0, 0, 0, 0, 0, 0 ]71

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 3 ]
Characteristic: not 2,3,19
Dimension: 952

Level   dominant weight   weight multiplicity   length of W-orbit 
49[ 0, 0, 0, 0, 0, 0, 0, 3 ]116
47[ 0, 0, 0, 0, 0, 0, 1, 1 ]1224
43[ 0, 0, 0, 0, 0, 1, 0, 0 ]1448
33[ 0, 0, 0, 0, 0, 0, 0, 2 ]116
31[ 0, 0, 0, 0, 0, 0, 1, 0 ]1112
17[ 0, 0, 0, 0, 0, 0, 0, 1 ]816
1[ 0, 0, 0, 0, 0, 0, 0, 0 ]81

Highest weight: [ 0, 0, 0, 0, 0, 0, 1, 1 ]
Characteristic: 2
Dimension: 1344

Level   dominant weight   weight multiplicity   length of W-orbit 
47[ 0, 0, 0, 0, 0, 0, 1, 1 ]1224
43[ 0, 0, 0, 0, 0, 1, 0, 0 ]2448
17[ 0, 0, 0, 0, 0, 0, 0, 1 ]1416

Highest weight: [ 0, 0, 0, 0, 1, 0, 0, 0 ]
Characteristic: 2
Dimension: 1582

Level   dominant weight   weight multiplicity   length of W-orbit 
53[ 0, 0, 0, 0, 1, 0, 0, 0 ]11120
31[ 0, 0, 0, 0, 0, 0, 1, 0 ]4112
1[ 0, 0, 0, 0, 0, 0, 0, 0 ]141

Highest weight: [ 0, 0, 0, 0, 0, 0, 1, 1 ]
Characteristic: not 2,3
Dimension: 1615

Level   dominant weight   weight multiplicity   length of W-orbit 
47[ 0, 0, 0, 0, 0, 0, 1, 1 ]1224
43[ 0, 0, 0, 0, 0, 1, 0, 0 ]2448
33[ 0, 0, 0, 0, 0, 0, 0, 2 ]116
31[ 0, 0, 0, 0, 0, 0, 1, 0 ]2112
17[ 0, 0, 0, 0, 0, 0, 0, 1 ]1516
1[ 0, 0, 0, 0, 0, 0, 0, 0 ]151

Highest weight: [ 0, 0, 0, 0, 1, 0, 0, 0 ]
Characteristic: not 2
Dimension: 2380

Level   dominant weight   weight multiplicity   length of W-orbit 
53[ 0, 0, 0, 0, 1, 0, 0, 0 ]11120
43[ 0, 0, 0, 0, 0, 1, 0, 0 ]1448
31[ 0, 0, 0, 0, 0, 0, 1, 0 ]6112
17[ 0, 0, 0, 0, 0, 0, 0, 1 ]716
1[ 0, 0, 0, 0, 0, 0, 0, 0 ]281

Highest weight: [ 0, 0, 0, 1, 0, 0, 0, 0 ]
Characteristic: 2
Dimension: 3808

Level   dominant weight   weight multiplicity   length of W-orbit 
61[ 0, 0, 0, 1, 0, 0, 0, 0 ]11792
43[ 0, 0, 0, 0, 0, 1, 0, 0 ]4448
17[ 0, 0, 0, 0, 0, 0, 0, 1 ]1416

Highest weight: [ 1, 0, 0, 0, 0, 0, 0, 1 ]
Characteristic: 17
Dimension: 3840

Level   dominant weight   weight multiplicity   length of W-orbit 
53[ 1, 0, 0, 0, 0, 0, 0, 1 ]12048
37[ 1, 0, 0, 0, 0, 0, 0, 0 ]7256

Highest weight: [ 1, 0, 0, 0, 0, 0, 0, 1 ]
Characteristic: not 17
Dimension: 4096

Level   dominant weight   weight multiplicity   length of W-orbit 
53[ 1, 0, 0, 0, 0, 0, 0, 1 ]12048
37[ 1, 0, 0, 0, 0, 0, 0, 0 ]8256

Highest weight: [ 0, 0, 0, 0, 0, 0, 2, 0 ]
Characteristic: 3
Dimension: 4251

Level   dominant weight   weight multiplicity   length of W-orbit 
61[ 0, 0, 0, 0, 0, 0, 2, 0 ]1112
59[ 0, 0, 0, 0, 0, 1, 0, 1 ]11344
53[ 0, 0, 0, 0, 1, 0, 0, 0 ]11120
47[ 0, 0, 0, 0, 0, 0, 1, 1 ]1224
43[ 0, 0, 0, 0, 0, 1, 0, 0 ]1448
33[ 0, 0, 0, 0, 0, 0, 0, 2 ]616
31[ 0, 0, 0, 0, 0, 0, 1, 0 ]7112
17[ 0, 0, 0, 0, 0, 0, 0, 1 ]616
1[ 0, 0, 0, 0, 0, 0, 0, 0 ]271

Highest weight: [ 0, 0, 1, 0, 0, 0, 0, 0 ]
Characteristic: 2
Dimension: 4488

Level   dominant weight   weight multiplicity   length of W-orbit 
67[ 0, 0, 1, 0, 0, 0, 0, 0 ]11792
53[ 0, 0, 0, 0, 1, 0, 0, 0 ]21120
31[ 0, 0, 0, 0, 0, 0, 1, 0 ]4112
1[ 0, 0, 0, 0, 0, 0, 0, 0 ]81

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 4 ]
Characteristic: 7
Dimension: 4540

Level   dominant weight   weight multiplicity   length of W-orbit 
65[ 0, 0, 0, 0, 0, 0, 0, 4 ]116
63[ 0, 0, 0, 0, 0, 0, 1, 2 ]1224
61[ 0, 0, 0, 0, 0, 0, 2, 0 ]1112
59[ 0, 0, 0, 0, 0, 1, 0, 1 ]11344
53[ 0, 0, 0, 0, 1, 0, 0, 0 ]11120
49[ 0, 0, 0, 0, 0, 0, 0, 3 ]116
47[ 0, 0, 0, 0, 0, 0, 1, 1 ]1224
43[ 0, 0, 0, 0, 0, 1, 0, 0 ]1448
33[ 0, 0, 0, 0, 0, 0, 0, 2 ]716
31[ 0, 0, 0, 0, 0, 0, 1, 0 ]7112
17[ 0, 0, 0, 0, 0, 0, 0, 1 ]716
1[ 0, 0, 0, 0, 0, 0, 0, 0 ]281

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 4 ]
Characteristic: 19
Dimension: 4691

Level   dominant weight   weight multiplicity   length of W-orbit 
65[ 0, 0, 0, 0, 0, 0, 0, 4 ]116
63[ 0, 0, 0, 0, 0, 0, 1, 2 ]1224
61[ 0, 0, 0, 0, 0, 0, 2, 0 ]1112
59[ 0, 0, 0, 0, 0, 1, 0, 1 ]11344
53[ 0, 0, 0, 0, 1, 0, 0, 0 ]11120
49[ 0, 0, 0, 0, 0, 0, 0, 3 ]116
47[ 0, 0, 0, 0, 0, 0, 1, 1 ]1224
43[ 0, 0, 0, 0, 0, 1, 0, 0 ]1448
33[ 0, 0, 0, 0, 0, 0, 0, 2 ]816
31[ 0, 0, 0, 0, 0, 0, 1, 0 ]8112
17[ 0, 0, 0, 0, 0, 0, 0, 1 ]816
1[ 0, 0, 0, 0, 0, 0, 0, 0 ]351

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 4 ]
Characteristic: not 2,3,7,19
Dimension: 4692

Level   dominant weight   weight multiplicity   length of W-orbit 
65[ 0, 0, 0, 0, 0, 0, 0, 4 ]116
63[ 0, 0, 0, 0, 0, 0, 1, 2 ]1224
61[ 0, 0, 0, 0, 0, 0, 2, 0 ]1112
59[ 0, 0, 0, 0, 0, 1, 0, 1 ]11344
53[ 0, 0, 0, 0, 1, 0, 0, 0 ]11120
49[ 0, 0, 0, 0, 0, 0, 0, 3 ]116
47[ 0, 0, 0, 0, 0, 0, 1, 1 ]1224
43[ 0, 0, 0, 0, 0, 1, 0, 0 ]1448
33[ 0, 0, 0, 0, 0, 0, 0, 2 ]816
31[ 0, 0, 0, 0, 0, 0, 1, 0 ]8112
17[ 0, 0, 0, 0, 0, 0, 0, 1 ]816
1[ 0, 0, 0, 0, 0, 0, 0, 0 ]361

Highest weight: [ 0, 0, 0, 0, 0, 1, 0, 1 ]
Characteristic: 2
Dimension: 5066

Level   dominant weight   weight multiplicity   length of W-orbit 
59[ 0, 0, 0, 0, 0, 1, 0, 1 ]11344
53[ 0, 0, 0, 0, 1, 0, 0, 0 ]21120
33[ 0, 0, 0, 0, 0, 0, 0, 2 ]616
31[ 0, 0, 0, 0, 0, 0, 1, 0 ]12112
1[ 0, 0, 0, 0, 0, 0, 0, 0 ]421

Highest weight: [ 0, 0, 0, 1, 0, 0, 0, 0 ]
Characteristic: not 2
Dimension: 6188

Level   dominant weight   weight multiplicity   length of W-orbit 
61[ 0, 0, 0, 1, 0, 0, 0, 0 ]11792
53[ 0, 0, 0, 0, 1, 0, 0, 0 ]11120
43[ 0, 0, 0, 0, 0, 1, 0, 0 ]5448
31[ 0, 0, 0, 0, 0, 0, 1, 0 ]6112
17[ 0, 0, 0, 0, 0, 0, 0, 1 ]2116
1[ 0, 0, 0, 0, 0, 0, 0, 0 ]281

Highest weight: [ 0, 1, 0, 0, 0, 0, 0, 0 ]
Characteristic: 2
Dimension: 6528

Level   dominant weight   weight multiplicity   length of W-orbit 
71[ 0, 1, 0, 0, 0, 0, 0, 0 ]11024
61[ 0, 0, 0, 1, 0, 0, 0, 0 ]21792
43[ 0, 0, 0, 0, 0, 1, 0, 0 ]4448
17[ 0, 0, 0, 0, 0, 0, 0, 1 ]816

Highest weight: [ 0, 0, 0, 0, 0, 0, 2, 0 ]
Characteristic: 5
Dimension: 6631

Level   dominant weight   weight multiplicity   length of W-orbit 
61[ 0, 0, 0, 0, 0, 0, 2, 0 ]1112
59[ 0, 0, 0, 0, 0, 1, 0, 1 ]11344
53[ 0, 0, 0, 0, 1, 0, 0, 0 ]21120
47[ 0, 0, 0, 0, 0, 0, 1, 1 ]1224
43[ 0, 0, 0, 0, 0, 1, 0, 0 ]2448
33[ 0, 0, 0, 0, 0, 0, 0, 2 ]616
31[ 0, 0, 0, 0, 0, 0, 1, 0 ]13112
17[ 0, 0, 0, 0, 0, 0, 0, 1 ]1316
1[ 0, 0, 0, 0, 0, 0, 0, 0 ]551

Highest weight: [ 0, 0, 0, 0, 0, 0, 2, 0 ]
Characteristic: not 2,3,5
Dimension: 6783

Level   dominant weight   weight multiplicity   length of W-orbit 
61[ 0, 0, 0, 0, 0, 0, 2, 0 ]1112
59[ 0, 0, 0, 0, 0, 1, 0, 1 ]11344
53[ 0, 0, 0, 0, 1, 0, 0, 0 ]21120
47[ 0, 0, 0, 0, 0, 0, 1, 1 ]1224
43[ 0, 0, 0, 0, 0, 1, 0, 0 ]2448
33[ 0, 0, 0, 0, 0, 0, 0, 2 ]716
31[ 0, 0, 0, 0, 0, 0, 1, 0 ]14112
17[ 0, 0, 0, 0, 0, 0, 0, 1 ]1416
1[ 0, 0, 0, 0, 0, 0, 0, 0 ]631