Weight Multiplicities

Groups of type A5, all 2-restricted highest weights in characteristic 2

Diagram:

1 - 2 - 3 - 4 - 5

Overview

Dimension	Highest weight	Characteristic
1	[ 0, 0, 0, 0, 0 ]	2
6	[ 0, 0, 0, 0, 1 ]	2
6	[ 1, 0, 0, 0, 0 ]	2
15	[ 0, 0, 0, 1, 0 ]	2
15	[ 0, 1, 0, 0, 0 ]	2
20	[ 0, 0, 1, 0, 0 ]	2
34	[ 1, 0, 0, 0, 1 ]	2
70	[ 0, 0, 0, 1, 1 ]	2
70	[ 1, 1, 0, 0, 0 ]	2
84	[ 0, 1, 0, 0, 1 ]	2
84	[ 1, 0, 0, 1, 0 ]	2
90	[ 0, 0, 1, 0, 1 ]	2
90	[ 1, 0, 1, 0, 0 ]	2
154	[ 0, 1, 0, 1, 0 ]	2
204	[ 0, 0, 1, 1, 0 ]	2
204	[ 0, 1, 1, 0, 0 ]	2
384	[ 1, 0, 0, 1, 1 ]	2
384	[ 1, 1, 0, 0, 1 ]	2
400	[ 1, 0, 1, 0, 1 ]	2
720	[ 0, 1, 0, 1, 1 ]	2
720	[ 1, 1, 0, 1, 0 ]	2
896	[ 0, 0, 1, 1, 1 ]	2
896	[ 1, 1, 1, 0, 0 ]	2
924	[ 0, 1, 1, 0, 1 ]	2
924	[ 1, 0, 1, 1, 0 ]	2
1960	[ 0, 1, 1, 1, 0 ]	2
3114	[ 1, 1, 0, 1, 1 ]	2
3984	[ 1, 0, 1, 1, 1 ]	2
3984	[ 1, 1, 1, 0, 1 ]	2
8064	[ 0, 1, 1, 1, 1 ]	2
8064	[ 1, 1, 1, 1, 0 ]	2
32768	[ 1, 1, 1, 1, 1 ]	2

The characters

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

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

Highest weight: [ 0, 0, 0, 0, 1 ]
Characteristic: 2
Dimension: 6

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

Highest weight: [ 1, 0, 0, 0, 0 ]
Characteristic: 2
Dimension: 6

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

Highest weight: [ 0, 0, 0, 1, 0 ]
Characteristic: 2
Dimension: 15

Level	dominant weight	weight multiplicity	length of W-orbit
9	[ 0, 0, 0, 1, 0 ]	1	15

Highest weight: [ 0, 1, 0, 0, 0 ]
Characteristic: 2
Dimension: 15

Level	dominant weight	weight multiplicity	length of W-orbit
9	[ 0, 1, 0, 0, 0 ]	1	15

Highest weight: [ 0, 0, 1, 0, 0 ]
Characteristic: 2
Dimension: 20

Level	dominant weight	weight multiplicity	length of W-orbit
10	[ 0, 0, 1, 0, 0 ]	1	20

Highest weight: [ 1, 0, 0, 0, 1 ]
Characteristic: 2
Dimension: 34

Level	dominant weight	weight multiplicity	length of W-orbit
11	[ 1, 0, 0, 0, 1 ]	1	30
1	[ 0, 0, 0, 0, 0 ]	4	1

Highest weight: [ 0, 0, 0, 1, 1 ]
Characteristic: 2
Dimension: 70

Level	dominant weight	weight multiplicity	length of W-orbit
14	[ 0, 0, 0, 1, 1 ]	1	30
10	[ 0, 0, 1, 0, 0 ]	2	20

Highest weight: [ 1, 1, 0, 0, 0 ]
Characteristic: 2
Dimension: 70

Level	dominant weight	weight multiplicity	length of W-orbit
14	[ 1, 1, 0, 0, 0 ]	1	30
10	[ 0, 0, 1, 0, 0 ]	2	20

Highest weight: [ 0, 1, 0, 0, 1 ]
Characteristic: 2
Dimension: 84

Level	dominant weight	weight multiplicity	length of W-orbit
14	[ 0, 1, 0, 0, 1 ]	1	60
6	[ 1, 0, 0, 0, 0 ]	4	6

Highest weight: [ 1, 0, 0, 1, 0 ]
Characteristic: 2
Dimension: 84

Level	dominant weight	weight multiplicity	length of W-orbit
14	[ 1, 0, 0, 1, 0 ]	1	60
6	[ 0, 0, 0, 0, 1 ]	4	6

Highest weight: [ 0, 0, 1, 0, 1 ]
Characteristic: 2
Dimension: 90

Level	dominant weight	weight multiplicity	length of W-orbit
15	[ 0, 0, 1, 0, 1 ]	1	60
9	[ 0, 1, 0, 0, 0 ]	2	15

Highest weight: [ 1, 0, 1, 0, 0 ]
Characteristic: 2
Dimension: 90

Level	dominant weight	weight multiplicity	length of W-orbit
15	[ 1, 0, 1, 0, 0 ]	1	60
9	[ 0, 0, 0, 1, 0 ]	2	15

Highest weight: [ 0, 1, 0, 1, 0 ]
Characteristic: 2
Dimension: 154

Level	dominant weight	weight multiplicity	length of W-orbit
17	[ 0, 1, 0, 1, 0 ]	1	90
11	[ 1, 0, 0, 0, 1 ]	2	30
1	[ 0, 0, 0, 0, 0 ]	4	1

Highest weight: [ 0, 0, 1, 1, 0 ]
Characteristic: 2
Dimension: 204

Level	dominant weight	weight multiplicity	length of W-orbit
18	[ 0, 0, 1, 1, 0 ]	1	60
14	[ 0, 1, 0, 0, 1 ]	2	60
6	[ 1, 0, 0, 0, 0 ]	4	6

Highest weight: [ 0, 1, 1, 0, 0 ]
Characteristic: 2
Dimension: 204

Level	dominant weight	weight multiplicity	length of W-orbit
18	[ 0, 1, 1, 0, 0 ]	1	60
14	[ 1, 0, 0, 1, 0 ]	2	60
6	[ 0, 0, 0, 0, 1 ]	4	6

Highest weight: [ 1, 0, 0, 1, 1 ]
Characteristic: 2
Dimension: 384

Level	dominant weight	weight multiplicity	length of W-orbit
19	[ 1, 0, 0, 1, 1 ]	1	120
15	[ 1, 0, 1, 0, 0 ]	2	60
11	[ 0, 0, 0, 0, 2 ]	4	6
9	[ 0, 0, 0, 1, 0 ]	8	15

Highest weight: [ 1, 1, 0, 0, 1 ]
Characteristic: 2
Dimension: 384

Level	dominant weight	weight multiplicity	length of W-orbit
19	[ 1, 1, 0, 0, 1 ]	1	120
15	[ 0, 0, 1, 0, 1 ]	2	60
11	[ 2, 0, 0, 0, 0 ]	4	6
9	[ 0, 1, 0, 0, 0 ]	8	15

Highest weight: [ 1, 0, 1, 0, 1 ]
Characteristic: 2
Dimension: 400

Level	dominant weight	weight multiplicity	length of W-orbit
20	[ 1, 0, 1, 0, 1 ]	1	180
14	[ 1, 1, 0, 0, 0 ]	2	30
14	[ 0, 0, 0, 1, 1 ]	2	30
10	[ 0, 0, 1, 0, 0 ]	5	20

Highest weight: [ 0, 1, 0, 1, 1 ]
Characteristic: 2
Dimension: 720

Level	dominant weight	weight multiplicity	length of W-orbit
22	[ 0, 1, 0, 1, 1 ]	1	180
18	[ 0, 1, 1, 0, 0 ]	2	60
16	[ 1, 0, 0, 0, 2 ]	2	30
14	[ 1, 0, 0, 1, 0 ]	5	60
6	[ 0, 0, 0, 0, 1 ]	10	6

Highest weight: [ 1, 1, 0, 1, 0 ]
Characteristic: 2
Dimension: 720

Level	dominant weight	weight multiplicity	length of W-orbit
22	[ 1, 1, 0, 1, 0 ]	1	180
18	[ 0, 0, 1, 1, 0 ]	2	60
16	[ 2, 0, 0, 0, 1 ]	2	30
14	[ 0, 1, 0, 0, 1 ]	5	60
6	[ 1, 0, 0, 0, 0 ]	10	6

Highest weight: [ 0, 0, 1, 1, 1 ]
Characteristic: 2
Dimension: 896

Level	dominant weight	weight multiplicity	length of W-orbit
23	[ 0, 0, 1, 1, 1 ]	1	120
19	[ 0, 1, 0, 0, 2 ]	2	60
19	[ 0, 0, 2, 0, 0 ]	2	20
17	[ 0, 1, 0, 1, 0 ]	4	90
11	[ 1, 0, 0, 0, 1 ]	8	30
1	[ 0, 0, 0, 0, 0 ]	16	1

Highest weight: [ 1, 1, 1, 0, 0 ]
Characteristic: 2
Dimension: 896

Level	dominant weight	weight multiplicity	length of W-orbit
23	[ 1, 1, 1, 0, 0 ]	1	120
19	[ 2, 0, 0, 1, 0 ]	2	60
19	[ 0, 0, 2, 0, 0 ]	2	20
17	[ 0, 1, 0, 1, 0 ]	4	90
11	[ 1, 0, 0, 0, 1 ]	8	30
1	[ 0, 0, 0, 0, 0 ]	16	1

Highest weight: [ 0, 1, 1, 0, 1 ]
Characteristic: 2
Dimension: 924

Level	dominant weight	weight multiplicity	length of W-orbit
23	[ 0, 1, 1, 0, 1 ]	1	180
19	[ 1, 0, 0, 1, 1 ]	2	120
17	[ 0, 2, 0, 0, 0 ]	2	15
15	[ 1, 0, 1, 0, 0 ]	5	60
11	[ 0, 0, 0, 0, 2 ]	4	6
9	[ 0, 0, 0, 1, 0 ]	10	15

Highest weight: [ 1, 0, 1, 1, 0 ]
Characteristic: 2
Dimension: 924

Level	dominant weight	weight multiplicity	length of W-orbit
23	[ 1, 0, 1, 1, 0 ]	1	180
19	[ 1, 1, 0, 0, 1 ]	2	120
17	[ 0, 0, 0, 2, 0 ]	2	15
15	[ 0, 0, 1, 0, 1 ]	5	60
11	[ 2, 0, 0, 0, 0 ]	4	6
9	[ 0, 1, 0, 0, 0 ]	10	15

Highest weight: [ 0, 1, 1, 1, 0 ]
Characteristic: 2
Dimension: 1960

Level	dominant weight	weight multiplicity	length of W-orbit
26	[ 0, 1, 1, 1, 0 ]	1	180
22	[ 1, 0, 0, 2, 0 ]	2	60
22	[ 0, 2, 0, 0, 1 ]	2	60
20	[ 1, 0, 1, 0, 1 ]	4	180
14	[ 1, 1, 0, 0, 0 ]	8	30
14	[ 0, 0, 0, 1, 1 ]	8	30
10	[ 0, 0, 1, 0, 0 ]	17	20

Highest weight: [ 1, 1, 0, 1, 1 ]
Characteristic: 2
Dimension: 3114

Level	dominant weight	weight multiplicity	length of W-orbit
27	[ 1, 1, 0, 1, 1 ]	1	360
23	[ 1, 1, 1, 0, 0 ]	2	120
23	[ 0, 0, 1, 1, 1 ]	2	120
21	[ 2, 0, 0, 0, 2 ]	2	30
19	[ 2, 0, 0, 1, 0 ]	5	60
19	[ 0, 1, 0, 0, 2 ]	5	60
19	[ 0, 0, 2, 0, 0 ]	4	20
17	[ 0, 1, 0, 1, 0 ]	10	90
11	[ 1, 0, 0, 0, 1 ]	20	30
1	[ 0, 0, 0, 0, 0 ]	34	1

Highest weight: [ 1, 0, 1, 1, 1 ]
Characteristic: 2
Dimension: 3984

Level	dominant weight	weight multiplicity	length of W-orbit
28	[ 1, 0, 1, 1, 1 ]	1	360
24	[ 1, 1, 0, 0, 2 ]	2	120
24	[ 1, 0, 2, 0, 0 ]	2	60
22	[ 1, 1, 0, 1, 0 ]	4	180
22	[ 0, 0, 0, 2, 1 ]	2	30
20	[ 0, 0, 1, 0, 2 ]	5	60
18	[ 0, 0, 1, 1, 0 ]	10	60
16	[ 2, 0, 0, 0, 1 ]	8	30
14	[ 0, 1, 0, 0, 1 ]	19	60
6	[ 1, 0, 0, 0, 0 ]	34	6

Highest weight: [ 1, 1, 1, 0, 1 ]
Characteristic: 2
Dimension: 3984

Level	dominant weight	weight multiplicity	length of W-orbit
28	[ 1, 1, 1, 0, 1 ]	1	360
24	[ 2, 0, 0, 1, 1 ]	2	120
24	[ 0, 0, 2, 0, 1 ]	2	60
22	[ 0, 1, 0, 1, 1 ]	4	180
22	[ 1, 2, 0, 0, 0 ]	2	30
20	[ 2, 0, 1, 0, 0 ]	5	60
18	[ 0, 1, 1, 0, 0 ]	10	60
16	[ 1, 0, 0, 0, 2 ]	8	30
14	[ 1, 0, 0, 1, 0 ]	19	60
6	[ 0, 0, 0, 0, 1 ]	34	6

Highest weight: [ 0, 1, 1, 1, 1 ]
Characteristic: 2
Dimension: 8064

Level	dominant weight	weight multiplicity	length of W-orbit
31	[ 0, 1, 1, 1, 1 ]	1	360
27	[ 1, 0, 0, 2, 1 ]	2	120
27	[ 0, 2, 0, 0, 2 ]	2	60
27	[ 0, 1, 2, 0, 0 ]	2	60
25	[ 1, 0, 1, 0, 2 ]	4	180
25	[ 0, 2, 0, 1, 0 ]	4	90
23	[ 1, 0, 1, 1, 0 ]	8	180
19	[ 1, 1, 0, 0, 1 ]	14	120
19	[ 0, 0, 0, 1, 2 ]	8	30
17	[ 0, 0, 0, 2, 0 ]	16	15
15	[ 0, 0, 1, 0, 1 ]	28	60
11	[ 2, 0, 0, 0, 0 ]	24	6
9	[ 0, 1, 0, 0, 0 ]	48	15

Highest weight: [ 1, 1, 1, 1, 0 ]
Characteristic: 2
Dimension: 8064

Level	dominant weight	weight multiplicity	length of W-orbit
31	[ 1, 1, 1, 1, 0 ]	1	360
27	[ 1, 2, 0, 0, 1 ]	2	120
27	[ 2, 0, 0, 2, 0 ]	2	60
27	[ 0, 0, 2, 1, 0 ]	2	60
25	[ 2, 0, 1, 0, 1 ]	4	180
25	[ 0, 1, 0, 2, 0 ]	4	90
23	[ 0, 1, 1, 0, 1 ]	8	180
19	[ 1, 0, 0, 1, 1 ]	14	120
19	[ 2, 1, 0, 0, 0 ]	8	30
17	[ 0, 2, 0, 0, 0 ]	16	15
15	[ 1, 0, 1, 0, 0 ]	28	60
11	[ 0, 0, 0, 0, 2 ]	24	6
9	[ 0, 0, 0, 1, 0 ]	48	15

Highest weight: [ 1, 1, 1, 1, 1 ]
Characteristic: 2
Dimension: 32768

Level	dominant weight	weight multiplicity	length of W-orbit
36	[ 1, 1, 1, 1, 1 ]	1	720
32	[ 2, 0, 0, 2, 1 ]	2	120
32	[ 1, 2, 0, 0, 2 ]	2	120
32	[ 1, 1, 2, 0, 0 ]	2	120
32	[ 0, 0, 2, 1, 1 ]	2	120
30	[ 2, 0, 1, 0, 2 ]	4	180
30	[ 1, 2, 0, 1, 0 ]	4	180
30	[ 0, 1, 0, 2, 1 ]	4	180
28	[ 0, 0, 3, 0, 0 ]	4	20
28	[ 2, 0, 1, 1, 0 ]	8	180
28	[ 0, 1, 1, 0, 2 ]	8	180
26	[ 0, 1, 1, 1, 0 ]	16	180
24	[ 2, 1, 0, 0, 1 ]	14	120
24	[ 1, 0, 0, 1, 2 ]	14	120
22	[ 1, 0, 0, 2, 0 ]	28	60
22	[ 0, 2, 0, 0, 1 ]	28	60
20	[ 1, 0, 1, 0, 1 ]	48	180
16	[ 3, 0, 0, 0, 0 ]	24	6
16	[ 0, 0, 0, 0, 3 ]	24	6
14	[ 1, 1, 0, 0, 0 ]	80	30
14	[ 0, 0, 0, 1, 1 ]	80	30
10	[ 0, 0, 1, 0, 0 ]	132	20