[Overview]

Weight Multiplicities

Groups of type C10, degree bound 10000

Diagram:

1 > o - .. - 10

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
188[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]5
189[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]not 2, 5
210[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]not 2
1024[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]2
1100[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]3
1120[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]not 3
1520[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]3
1540[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 3 ]not 2, 3
2620[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]7
2640[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]not 3, 7
4466[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ]2
4654[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ]3
4655[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ]not 2, 3
8455[ 0, 0, 0, 0, 0, 0, 0, 0, 2, 0 ]3
8855[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 4 ]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 
20[ 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 
37[ 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: 5
Dimension: 188

Level   dominant weight   weight multiplicity   length of W-orbit 
37[ 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 2,5
Dimension: 189

Level   dominant weight   weight multiplicity   length of W-orbit 
37[ 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, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]
Characteristic: not 2
Dimension: 210

Level   dominant weight   weight multiplicity   length of W-orbit 
39[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]120
37[ 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: [ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]
Characteristic: 2
Dimension: 1024

Level   dominant weight   weight multiplicity   length of W-orbit 
101[ 1, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]11024

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]
Characteristic: 3
Dimension: 1100

Level   dominant weight   weight multiplicity   length of W-orbit 
52[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]1960
20[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]720

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]
Characteristic: not 3
Dimension: 1120

Level   dominant weight   weight multiplicity   length of W-orbit 
52[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]1960
20[ 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: 1520

Level   dominant weight   weight multiplicity   length of W-orbit 
56[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]1360
52[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]1960
20[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]1020

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 3 ]
Characteristic: not 2,3
Dimension: 1540

Level   dominant weight   weight multiplicity   length of W-orbit 
58[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 3 ]120
56[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]1360
52[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]1960
20[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 1 ]1020

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]
Characteristic: 7
Dimension: 2620

Level   dominant weight   weight multiplicity   length of W-orbit 
56[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]1360
52[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]2960
20[ 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 3,7
Dimension: 2640

Level   dominant weight   weight multiplicity   length of W-orbit 
56[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 1 ]1360
52[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 0 ]2960
20[ 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 
65[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ]13360
37[ 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: 3
Dimension: 4654

Level   dominant weight   weight multiplicity   length of W-orbit 
65[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ]13360
37[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]7180
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]341

Highest weight: [ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ]
Characteristic: not 2,3
Dimension: 4655

Level   dominant weight   weight multiplicity   length of W-orbit 
65[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ]13360
37[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]7180
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]351

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 2, 0 ]
Characteristic: 3
Dimension: 8455

Level   dominant weight   weight multiplicity   length of W-orbit 
73[ 0, 0, 0, 0, 0, 0, 0, 0, 2, 0 ]1180
71[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1 ]12880
65[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ]13360
39[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]920
37[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]10180
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]551

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 0, 4 ]
Characteristic: not 2,3
Dimension: 8855

Level   dominant weight   weight multiplicity   length of W-orbit 
77[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 4 ]120
75[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 2 ]1360
73[ 0, 0, 0, 0, 0, 0, 0, 0, 2, 0 ]1180
71[ 0, 0, 0, 0, 0, 0, 0, 1, 0, 1 ]12880
65[ 0, 0, 0, 0, 0, 0, 1, 0, 0, 0 ]13360
39[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 2 ]1020
37[ 0, 0, 0, 0, 0, 0, 0, 0, 1, 0 ]10180
1[ 0, 0, 0, 0, 0, 0, 0, 0, 0, 0 ]551