Weight Multiplicities

Groups of type C9, degree bound 10000

Diagram:

1 > 2 - .. - 9

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 ]	1	1

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 1 ]
Characteristic: all
Dimension: 18

Level	dominant weight	weight multiplicity	length of W-orbit
18	[ 0, 0, 0, 0, 0, 0, 0, 0, 1 ]	1	18

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ]
Characteristic: 3
Dimension: 151

Level	dominant weight	weight multiplicity	length of W-orbit
33	[ 0, 0, 0, 0, 0, 0, 0, 1, 0 ]	1	144
1	[ 0, 0, 0, 0, 0, 0, 0, 0, 0 ]	7	1

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 1, 0 ]
Characteristic: not 3
Dimension: 152

Level	dominant weight	weight multiplicity	length of W-orbit
33	[ 0, 0, 0, 0, 0, 0, 0, 1, 0 ]	1	144
1	[ 0, 0, 0, 0, 0, 0, 0, 0, 0 ]	8	1

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 2 ]
Characteristic: not 2
Dimension: 171

Level	dominant weight	weight multiplicity	length of W-orbit
35	[ 0, 0, 0, 0, 0, 0, 0, 0, 2 ]	1	18
33	[ 0, 0, 0, 0, 0, 0, 0, 1, 0 ]	1	144
1	[ 0, 0, 0, 0, 0, 0, 0, 0, 0 ]	9	1

Highest weight: [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ]
Characteristic: 2
Dimension: 512

Level	dominant weight	weight multiplicity	length of W-orbit
82	[ 1, 0, 0, 0, 0, 0, 0, 0, 0 ]	1	512

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

Level	dominant weight	weight multiplicity	length of W-orbit
46	[ 0, 0, 0, 0, 0, 0, 1, 0, 0 ]	1	672
18	[ 0, 0, 0, 0, 0, 0, 0, 0, 1 ]	6	18

Highest weight: [ 0, 0, 0, 0, 0, 0, 1, 0, 0 ]
Characteristic: not 2
Dimension: 798

Level	dominant weight	weight multiplicity	length of W-orbit
46	[ 0, 0, 0, 0, 0, 0, 1, 0, 0 ]	1	672
18	[ 0, 0, 0, 0, 0, 0, 0, 0, 1 ]	7	18

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 1, 1 ]
Characteristic: 3
Dimension: 1122

Level	dominant weight	weight multiplicity	length of W-orbit
50	[ 0, 0, 0, 0, 0, 0, 0, 1, 1 ]	1	288
46	[ 0, 0, 0, 0, 0, 0, 1, 0, 0 ]	1	672
18	[ 0, 0, 0, 0, 0, 0, 0, 0, 1 ]	9	18

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 3 ]
Characteristic: not 2,3
Dimension: 1140

Level	dominant weight	weight multiplicity	length of W-orbit
52	[ 0, 0, 0, 0, 0, 0, 0, 0, 3 ]	1	18
50	[ 0, 0, 0, 0, 0, 0, 0, 1, 1 ]	1	288
46	[ 0, 0, 0, 0, 0, 0, 1, 0, 0 ]	1	672
18	[ 0, 0, 0, 0, 0, 0, 0, 0, 1 ]	9	18

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 1, 1 ]
Characteristic: 19
Dimension: 1902

Level	dominant weight	weight multiplicity	length of W-orbit
50	[ 0, 0, 0, 0, 0, 0, 0, 1, 1 ]	1	288
46	[ 0, 0, 0, 0, 0, 0, 1, 0, 0 ]	2	672
18	[ 0, 0, 0, 0, 0, 0, 0, 0, 1 ]	15	18

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 1, 1 ]
Characteristic: not 3,19
Dimension: 1920

Level	dominant weight	weight multiplicity	length of W-orbit
50	[ 0, 0, 0, 0, 0, 0, 0, 1, 1 ]	1	288
46	[ 0, 0, 0, 0, 0, 0, 1, 0, 0 ]	2	672
18	[ 0, 0, 0, 0, 0, 0, 0, 0, 1 ]	16	18

Highest weight: [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ]
Characteristic: 7
Dimension: 2755

Level	dominant weight	weight multiplicity	length of W-orbit
57	[ 0, 0, 0, 0, 0, 1, 0, 0, 0 ]	1	2016
33	[ 0, 0, 0, 0, 0, 0, 0, 1, 0 ]	5	144
1	[ 0, 0, 0, 0, 0, 0, 0, 0, 0 ]	19	1

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

Level	dominant weight	weight multiplicity	length of W-orbit
57	[ 0, 0, 0, 0, 0, 1, 0, 0, 0 ]	1	2016
33	[ 0, 0, 0, 0, 0, 0, 0, 1, 0 ]	6	144
1	[ 0, 0, 0, 0, 0, 0, 0, 0, 0 ]	26	1

Highest weight: [ 0, 0, 0, 0, 0, 1, 0, 0, 0 ]
Characteristic: not 2,7
Dimension: 2907

Level	dominant weight	weight multiplicity	length of W-orbit
57	[ 0, 0, 0, 0, 0, 1, 0, 0, 0 ]	1	2016
33	[ 0, 0, 0, 0, 0, 0, 0, 1, 0 ]	6	144
1	[ 0, 0, 0, 0, 0, 0, 0, 0, 0 ]	27	1

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 2, 0 ]
Characteristic: 3
Dimension: 5661

Level	dominant weight	weight multiplicity	length of W-orbit
65	[ 0, 0, 0, 0, 0, 0, 0, 2, 0 ]	1	144
63	[ 0, 0, 0, 0, 0, 0, 1, 0, 1 ]	1	2016
57	[ 0, 0, 0, 0, 0, 1, 0, 0, 0 ]	1	2016
35	[ 0, 0, 0, 0, 0, 0, 0, 0, 2 ]	8	18
33	[ 0, 0, 0, 0, 0, 0, 0, 1, 0 ]	9	144
1	[ 0, 0, 0, 0, 0, 0, 0, 0, 0 ]	45	1

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 0, 4 ]
Characteristic: not 2,3
Dimension: 5985

Level	dominant weight	weight multiplicity	length of W-orbit
69	[ 0, 0, 0, 0, 0, 0, 0, 0, 4 ]	1	18
67	[ 0, 0, 0, 0, 0, 0, 0, 1, 2 ]	1	288
65	[ 0, 0, 0, 0, 0, 0, 0, 2, 0 ]	1	144
63	[ 0, 0, 0, 0, 0, 0, 1, 0, 1 ]	1	2016
57	[ 0, 0, 0, 0, 0, 1, 0, 0, 0 ]	1	2016
35	[ 0, 0, 0, 0, 0, 0, 0, 0, 2 ]	9	18
33	[ 0, 0, 0, 0, 0, 0, 0, 1, 0 ]	9	144
1	[ 0, 0, 0, 0, 0, 0, 0, 0, 0 ]	45	1

Highest weight: [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ]
Characteristic: 3
Dimension: 6954

Level	dominant weight	weight multiplicity	length of W-orbit
66	[ 0, 0, 0, 0, 1, 0, 0, 0, 0 ]	1	4032
46	[ 0, 0, 0, 0, 0, 0, 1, 0, 0 ]	4	672
18	[ 0, 0, 0, 0, 0, 0, 0, 0, 1 ]	13	18

Highest weight: [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ]
Characteristic: 2
Dimension: 6972

Level	dominant weight	weight multiplicity	length of W-orbit
66	[ 0, 0, 0, 0, 1, 0, 0, 0, 0 ]	1	4032
46	[ 0, 0, 0, 0, 0, 0, 1, 0, 0 ]	4	672
18	[ 0, 0, 0, 0, 0, 0, 0, 0, 1 ]	14	18

Highest weight: [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ]
Characteristic: 7
Dimension: 7734

Level	dominant weight	weight multiplicity	length of W-orbit
66	[ 0, 0, 0, 0, 1, 0, 0, 0, 0 ]	1	4032
46	[ 0, 0, 0, 0, 0, 0, 1, 0, 0 ]	5	672
18	[ 0, 0, 0, 0, 0, 0, 0, 0, 1 ]	19	18

Highest weight: [ 0, 0, 0, 0, 1, 0, 0, 0, 0 ]
Characteristic: not 2,3,7
Dimension: 7752

Level	dominant weight	weight multiplicity	length of W-orbit
66	[ 0, 0, 0, 0, 1, 0, 0, 0, 0 ]	1	4032
46	[ 0, 0, 0, 0, 0, 0, 1, 0, 0 ]	5	672
18	[ 0, 0, 0, 0, 0, 0, 0, 0, 1 ]	20	18

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

Level	dominant weight	weight multiplicity	length of W-orbit
63	[ 0, 0, 0, 0, 0, 0, 1, 0, 1 ]	1	2016
57	[ 0, 0, 0, 0, 0, 1, 0, 0, 0 ]	2	2016
35	[ 0, 0, 0, 0, 0, 0, 0, 0, 2 ]	6	18
33	[ 0, 0, 0, 0, 0, 0, 0, 1, 0 ]	14	144
1	[ 0, 0, 0, 0, 0, 0, 0, 0, 0 ]	54	1

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 2, 0 ]
Characteristic: 5
Dimension: 8416

Level	dominant weight	weight multiplicity	length of W-orbit
65	[ 0, 0, 0, 0, 0, 0, 0, 2, 0 ]	1	144
63	[ 0, 0, 0, 0, 0, 0, 1, 0, 1 ]	1	2016
57	[ 0, 0, 0, 0, 0, 1, 0, 0, 0 ]	2	2016
35	[ 0, 0, 0, 0, 0, 0, 0, 0, 2 ]	8	18
33	[ 0, 0, 0, 0, 0, 0, 0, 1, 0 ]	14	144
1	[ 0, 0, 0, 0, 0, 0, 0, 0, 0 ]	64	1

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 2, 0 ]
Characteristic: 19
Dimension: 8567

Level	dominant weight	weight multiplicity	length of W-orbit
65	[ 0, 0, 0, 0, 0, 0, 0, 2, 0 ]	1	144
63	[ 0, 0, 0, 0, 0, 0, 1, 0, 1 ]	1	2016
57	[ 0, 0, 0, 0, 0, 1, 0, 0, 0 ]	2	2016
35	[ 0, 0, 0, 0, 0, 0, 0, 0, 2 ]	8	18
33	[ 0, 0, 0, 0, 0, 0, 0, 1, 0 ]	15	144
1	[ 0, 0, 0, 0, 0, 0, 0, 0, 0 ]	71	1

Highest weight: [ 0, 0, 0, 0, 0, 0, 0, 2, 0 ]
Characteristic: not 2,3,5,19
Dimension: 8568

Level	dominant weight	weight multiplicity	length of W-orbit
65	[ 0, 0, 0, 0, 0, 0, 0, 2, 0 ]	1	144
63	[ 0, 0, 0, 0, 0, 0, 1, 0, 1 ]	1	2016
57	[ 0, 0, 0, 0, 0, 1, 0, 0, 0 ]	2	2016
35	[ 0, 0, 0, 0, 0, 0, 0, 0, 2 ]	8	18
33	[ 0, 0, 0, 0, 0, 0, 0, 1, 0 ]	15	144
1	[ 0, 0, 0, 0, 0, 0, 0, 0, 0 ]	72	1

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

Level	dominant weight	weight multiplicity	length of W-orbit
99	[ 1, 0, 0, 0, 0, 0, 0, 0, 1 ]	1	4608
81	[ 0, 1, 0, 0, 0, 0, 0, 0, 0 ]	2	2304

Highest weight: [ 0, 1, 0, 0, 0, 0, 0, 0, 0 ]
Characteristic: 3
Dimension: 9841

Level	dominant weight	weight multiplicity	length of W-orbit
81	[ 0, 1, 0, 0, 0, 0, 0, 0, 0 ]	1	2304
73	[ 0, 0, 0, 1, 0, 0, 0, 0, 0 ]	1	5376
57	[ 0, 0, 0, 0, 0, 1, 0, 0, 0 ]	1	2016
33	[ 0, 0, 0, 0, 0, 0, 0, 1, 0 ]	1	144
1	[ 0, 0, 0, 0, 0, 0, 0, 0, 0 ]	1	1

Highest weight: [ 1, 0, 0, 0, 0, 0, 0, 0, 0 ]
Characteristic: 3
Dimension: 9842

Level	dominant weight	weight multiplicity	length of W-orbit
82	[ 1, 0, 0, 0, 0, 0, 0, 0, 0 ]	1	512
78	[ 0, 0, 1, 0, 0, 0, 0, 0, 0 ]	1	4608
66	[ 0, 0, 0, 0, 1, 0, 0, 0, 0 ]	1	4032
46	[ 0, 0, 0, 0, 0, 0, 1, 0, 0 ]	1	672
18	[ 0, 0, 0, 0, 0, 0, 0, 0, 1 ]	1	18