[Overview]

Weight Multiplicities

Groups of type E8, degree bound 500000

Diagram:

         2
         |
 1 - 3 - 4 - 5 - 6 - 7 - 8

Overview

DimensionHighest weightCharacteristic
1[ 0, 0, 0, 0, 0, 0, 0, 0 ]all
248[ 0, 0, 0, 0, 0, 0, 0, 1 ]all
3626[ 1, 0, 0, 0, 0, 0, 0, 0 ]2
3875[ 1, 0, 0, 0, 0, 0, 0, 0 ]not 2
23125[ 0, 0, 0, 0, 0, 0, 0, 2 ]7
26504[ 0, 0, 0, 0, 0, 0, 1, 0 ]2
26999[ 0, 0, 0, 0, 0, 0, 0, 2 ]31
27000[ 0, 0, 0, 0, 0, 0, 0, 2 ]not 2, 7, 31
30132[ 0, 0, 0, 0, 0, 0, 1, 0 ]3
30132[ 0, 0, 0, 0, 0, 0, 1, 0 ]5
30380[ 0, 0, 0, 0, 0, 0, 1, 0 ]not 2, 3, 5
113243[ 0, 1, 0, 0, 0, 0, 0, 0 ]3
143376[ 0, 1, 0, 0, 0, 0, 0, 0 ]2
147002[ 0, 1, 0, 0, 0, 0, 0, 0 ]7
147250[ 0, 1, 0, 0, 0, 0, 0, 0 ]not 2, 3, 7

The characters

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: all
Dimension: 248

Level   dominant weight   weight multiplicity   length of W-orbit 
59[ 0, 0, 0, 0, 0, 0, 0, 1 ]1240
1[ 0, 0, 0, 0, 0, 0, 0, 0 ]81

Highest weight: [ 1, 0, 0, 0, 0, 0, 0, 0 ]
Characteristic: 2
Dimension: 3626

Level   dominant weight   weight multiplicity   length of W-orbit 
93[ 1, 0, 0, 0, 0, 0, 0, 0 ]12160
59[ 0, 0, 0, 0, 0, 0, 0, 1 ]6240
1[ 0, 0, 0, 0, 0, 0, 0, 0 ]261

Highest weight: [ 1, 0, 0, 0, 0, 0, 0, 0 ]
Characteristic: not 2
Dimension: 3875

Level   dominant weight   weight multiplicity   length of W-orbit 
93[ 1, 0, 0, 0, 0, 0, 0, 0 ]12160
59[ 0, 0, 0, 0, 0, 0, 0, 1 ]7240
1[ 0, 0, 0, 0, 0, 0, 0, 0 ]351

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 2 ]
Characteristic: 7
Dimension: 23125

Level   dominant weight   weight multiplicity   length of W-orbit 
117[ 0, 0, 0, 0, 0, 0, 0, 2 ]1240
115[ 0, 0, 0, 0, 0, 0, 1, 0 ]16720
93[ 1, 0, 0, 0, 0, 0, 0, 0 ]52160
59[ 0, 0, 0, 0, 0, 0, 0, 1 ]22240
1[ 0, 0, 0, 0, 0, 0, 0, 0 ]851

Highest weight: [ 0, 0, 0, 0, 0, 0, 1, 0 ]
Characteristic: 2
Dimension: 26504

Level   dominant weight   weight multiplicity   length of W-orbit 
115[ 0, 0, 0, 0, 0, 0, 1, 0 ]16720
93[ 1, 0, 0, 0, 0, 0, 0, 0 ]62160
59[ 0, 0, 0, 0, 0, 0, 0, 1 ]28240
1[ 0, 0, 0, 0, 0, 0, 0, 0 ]1041

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 2 ]
Characteristic: 31
Dimension: 26999

Level   dominant weight   weight multiplicity   length of W-orbit 
117[ 0, 0, 0, 0, 0, 0, 0, 2 ]1240
115[ 0, 0, 0, 0, 0, 0, 1, 0 ]16720
93[ 1, 0, 0, 0, 0, 0, 0, 0 ]62160
59[ 0, 0, 0, 0, 0, 0, 0, 1 ]29240
1[ 0, 0, 0, 0, 0, 0, 0, 0 ]1191

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 2 ]
Characteristic: not 2,7,31
Dimension: 27000

Level   dominant weight   weight multiplicity   length of W-orbit 
117[ 0, 0, 0, 0, 0, 0, 0, 2 ]1240
115[ 0, 0, 0, 0, 0, 0, 1, 0 ]16720
93[ 1, 0, 0, 0, 0, 0, 0, 0 ]62160
59[ 0, 0, 0, 0, 0, 0, 0, 1 ]29240
1[ 0, 0, 0, 0, 0, 0, 0, 0 ]1201

Highest weight: [ 0, 0, 0, 0, 0, 0, 1, 0 ]
Characteristic: 3
Dimension: 30132

Level   dominant weight   weight multiplicity   length of W-orbit 
115[ 0, 0, 0, 0, 0, 0, 1, 0 ]16720
93[ 1, 0, 0, 0, 0, 0, 0, 0 ]72160
59[ 0, 0, 0, 0, 0, 0, 0, 1 ]34240
1[ 0, 0, 0, 0, 0, 0, 0, 0 ]1321

Highest weight: [ 0, 0, 0, 0, 0, 0, 1, 0 ]
Characteristic: 5
Dimension: 30132

Level   dominant weight   weight multiplicity   length of W-orbit 
115[ 0, 0, 0, 0, 0, 0, 1, 0 ]16720
93[ 1, 0, 0, 0, 0, 0, 0, 0 ]72160
59[ 0, 0, 0, 0, 0, 0, 0, 1 ]34240
1[ 0, 0, 0, 0, 0, 0, 0, 0 ]1321

Highest weight: [ 0, 0, 0, 0, 0, 0, 1, 0 ]
Characteristic: not 2,3,5
Dimension: 30380

Level   dominant weight   weight multiplicity   length of W-orbit 
115[ 0, 0, 0, 0, 0, 0, 1, 0 ]16720
93[ 1, 0, 0, 0, 0, 0, 0, 0 ]72160
59[ 0, 0, 0, 0, 0, 0, 0, 1 ]35240
1[ 0, 0, 0, 0, 0, 0, 0, 0 ]1401

Highest weight: [ 0, 1, 0, 0, 0, 0, 0, 0 ]
Characteristic: 3
Dimension: 113243

Level   dominant weight   weight multiplicity   length of W-orbit 
137[ 0, 1, 0, 0, 0, 0, 0, 0 ]117280
115[ 0, 0, 0, 0, 0, 0, 1, 0 ]56720
93[ 1, 0, 0, 0, 0, 0, 0, 0 ]212160
59[ 0, 0, 0, 0, 0, 0, 0, 1 ]70240
1[ 0, 0, 0, 0, 0, 0, 0, 0 ]2031

Highest weight: [ 0, 1, 0, 0, 0, 0, 0, 0 ]
Characteristic: 2
Dimension: 143376

Level   dominant weight   weight multiplicity   length of W-orbit 
137[ 0, 1, 0, 0, 0, 0, 0, 0 ]117280
115[ 0, 0, 0, 0, 0, 0, 1, 0 ]66720
93[ 1, 0, 0, 0, 0, 0, 0, 0 ]282160
59[ 0, 0, 0, 0, 0, 0, 0, 1 ]104240
1[ 0, 0, 0, 0, 0, 0, 0, 0 ]3361

Highest weight: [ 0, 1, 0, 0, 0, 0, 0, 0 ]
Characteristic: 7
Dimension: 147002

Level   dominant weight   weight multiplicity   length of W-orbit 
137[ 0, 1, 0, 0, 0, 0, 0, 0 ]117280
115[ 0, 0, 0, 0, 0, 0, 1, 0 ]66720
93[ 1, 0, 0, 0, 0, 0, 0, 0 ]292160
59[ 0, 0, 0, 0, 0, 0, 0, 1 ]110240
1[ 0, 0, 0, 0, 0, 0, 0, 0 ]3621

Highest weight: [ 0, 1, 0, 0, 0, 0, 0, 0 ]
Characteristic: not 2,3,7
Dimension: 147250

Level   dominant weight   weight multiplicity   length of W-orbit 
137[ 0, 1, 0, 0, 0, 0, 0, 0 ]117280
115[ 0, 0, 0, 0, 0, 0, 1, 0 ]66720
93[ 1, 0, 0, 0, 0, 0, 0, 0 ]292160
59[ 0, 0, 0, 0, 0, 0, 0, 1 ]111240
1[ 0, 0, 0, 0, 0, 0, 0, 0 ]3701