[Overview]

Weight Multiplicities

Groups of type F4, all 2-restricted highest weights in characteristic 2

Diagram:

1 - 2 > 3 - 4

Overview

DimensionHighest weightCharacteristic
1[ 0, 0, 0, 0 ]2
26[ 0, 0, 0, 1 ]2
26[ 1, 0, 0, 0 ]2
246[ 0, 0, 1, 0 ]2
676[ 1, 0, 0, 1 ]2
246[ 0, 1, 0, 0 ]2
4096[ 0, 0, 1, 1 ]2
6396[ 1, 0, 1, 0 ]2
6396[ 0, 1, 0, 1 ]2
4096[ 1, 1, 0, 0 ]2
106496[ 1, 0, 1, 1 ]2
60516[ 0, 1, 1, 0 ]2
106496[ 1, 1, 0, 1 ]2
1007616[ 0, 1, 1, 1 ]2
1007616[ 1, 1, 1, 0 ]2
16777216[ 1, 1, 1, 1 ]2

The characters

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

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

Highest weight: [ 0, 0, 0, 1 ]
Characteristic: 2
Dimension: 26

Level   dominant weight   weight multiplicity   length of W-orbit 
17[ 0, 0, 0, 1 ]124
1[ 0, 0, 0, 0 ]21

Highest weight: [ 1, 0, 0, 0 ]
Characteristic: 2
Dimension: 26

Level   dominant weight   weight multiplicity   length of W-orbit 
23[ 1, 0, 0, 0 ]124
1[ 0, 0, 0, 0 ]21

Highest weight: [ 0, 0, 1, 0 ]
Characteristic: 2
Dimension: 246

Level   dominant weight   weight multiplicity   length of W-orbit 
31[ 0, 0, 1, 0 ]196
23[ 1, 0, 0, 0 ]224
17[ 0, 0, 0, 1 ]424
1[ 0, 0, 0, 0 ]61

Highest weight: [ 1, 0, 0, 1 ]
Characteristic: 2
Dimension: 676

Level   dominant weight   weight multiplicity   length of W-orbit 
39[ 1, 0, 0, 1 ]1144
31[ 0, 0, 1, 0 ]396
23[ 1, 0, 0, 0 ]224
17[ 0, 0, 0, 1 ]824
1[ 0, 0, 0, 0 ]41

Highest weight: [ 0, 1, 0, 0 ]
Characteristic: 2
Dimension: 246

Level   dominant weight   weight multiplicity   length of W-orbit 
43[ 0, 1, 0, 0 ]196
33[ 0, 0, 0, 2 ]224
23[ 1, 0, 0, 0 ]424
1[ 0, 0, 0, 0 ]61

Highest weight: [ 0, 0, 1, 1 ]
Characteristic: 2
Dimension: 4096

Level   dominant weight   weight multiplicity   length of W-orbit 
47[ 0, 0, 1, 1 ]1192
43[ 0, 1, 0, 0 ]296
39[ 1, 0, 0, 1 ]4144
33[ 0, 0, 0, 2 ]824
31[ 0, 0, 1, 0 ]1496
23[ 1, 0, 0, 0 ]2424
17[ 0, 0, 0, 1 ]4024
1[ 0, 0, 0, 0 ]641

Highest weight: [ 1, 0, 1, 0 ]
Characteristic: 2
Dimension: 6396

Level   dominant weight   weight multiplicity   length of W-orbit 
53[ 1, 0, 1, 0 ]1288
47[ 0, 0, 1, 1 ]3192
45[ 2, 0, 0, 0 ]224
43[ 0, 1, 0, 0 ]496
39[ 1, 0, 0, 1 ]8144
33[ 0, 0, 0, 2 ]1224
31[ 0, 0, 1, 0 ]2096
23[ 1, 0, 0, 0 ]2624
17[ 0, 0, 0, 1 ]4424
1[ 0, 0, 0, 0 ]601

Highest weight: [ 0, 1, 0, 1 ]
Characteristic: 2
Dimension: 6396

Level   dominant weight   weight multiplicity   length of W-orbit 
59[ 0, 1, 0, 1 ]1288
53[ 1, 0, 1, 0 ]2288
49[ 0, 0, 0, 3 ]224
47[ 0, 0, 1, 1 ]5192
43[ 0, 1, 0, 0 ]296
39[ 1, 0, 0, 1 ]10144
33[ 0, 0, 0, 2 ]424
31[ 0, 0, 1, 0 ]1996
23[ 1, 0, 0, 0 ]824
17[ 0, 0, 0, 1 ]3224
1[ 0, 0, 0, 0 ]121

Highest weight: [ 1, 1, 0, 0 ]
Characteristic: 2
Dimension: 4096

Level   dominant weight   weight multiplicity   length of W-orbit 
65[ 1, 1, 0, 0 ]1192
61[ 0, 0, 2, 0 ]296
55[ 1, 0, 0, 2 ]4144
45[ 2, 0, 0, 0 ]824
43[ 0, 1, 0, 0 ]1496
33[ 0, 0, 0, 2 ]2424
23[ 1, 0, 0, 0 ]4024
1[ 0, 0, 0, 0 ]641

Highest weight: [ 1, 0, 1, 1 ]
Characteristic: 2
Dimension: 106496

Level   dominant weight   weight multiplicity   length of W-orbit 
69[ 1, 0, 1, 1 ]1576
65[ 1, 1, 0, 0 ]2192
63[ 0, 0, 1, 2 ]3192
61[ 2, 0, 0, 1 ]4144
61[ 0, 0, 2, 0 ]696
59[ 0, 1, 0, 1 ]10288
55[ 1, 0, 0, 2 ]16144
53[ 1, 0, 1, 0 ]26288
49[ 0, 0, 0, 3 ]2424
47[ 0, 0, 1, 1 ]59192
45[ 2, 0, 0, 0 ]4024
43[ 0, 1, 0, 0 ]8896
39[ 1, 0, 0, 1 ]128144
33[ 0, 0, 0, 2 ]18424
31[ 0, 0, 1, 0 ]26296
23[ 1, 0, 0, 0 ]36824
17[ 0, 0, 0, 1 ]51224
1[ 0, 0, 0, 0 ]7041

Highest weight: [ 0, 1, 1, 0 ]
Characteristic: 2
Dimension: 60516

Level   dominant weight   weight multiplicity   length of W-orbit 
73[ 0, 1, 1, 0 ]1288
69[ 1, 0, 1, 1 ]2576
65[ 1, 1, 0, 0 ]2192
63[ 0, 0, 1, 2 ]5192
61[ 2, 0, 0, 1 ]4144
61[ 0, 0, 2, 0 ]696
59[ 0, 1, 0, 1 ]10288
55[ 1, 0, 0, 2 ]12144
53[ 1, 0, 1, 0 ]21288
49[ 0, 0, 0, 3 ]2024
47[ 0, 0, 1, 1 ]40192
45[ 2, 0, 0, 0 ]2424
43[ 0, 1, 0, 0 ]4696
39[ 1, 0, 0, 1 ]72144
33[ 0, 0, 0, 2 ]8424
31[ 0, 0, 1, 0 ]12496
23[ 1, 0, 0, 0 ]14024
17[ 0, 0, 0, 1 ]20424
1[ 0, 0, 0, 0 ]2281

Highest weight: [ 1, 1, 0, 1 ]
Characteristic: 2
Dimension: 106496

Level   dominant weight   weight multiplicity   length of W-orbit 
81[ 1, 1, 0, 1 ]1576
77[ 0, 0, 2, 1 ]2192
75[ 2, 0, 1, 0 ]2288
73[ 0, 1, 1, 0 ]4288
71[ 1, 0, 0, 3 ]4144
69[ 1, 0, 1, 1 ]8576
65[ 1, 1, 0, 0 ]2192
63[ 0, 0, 1, 2 ]14192
61[ 2, 0, 0, 1 ]16144
61[ 0, 0, 2, 0 ]496
59[ 0, 1, 0, 1 ]28288
55[ 1, 0, 0, 2 ]8144
53[ 1, 0, 1, 0 ]48288
49[ 0, 0, 0, 3 ]4824
47[ 0, 0, 1, 1 ]80192
45[ 2, 0, 0, 0 ]1624
43[ 0, 1, 0, 0 ]2896
39[ 1, 0, 0, 1 ]132144
33[ 0, 0, 0, 2 ]4824
31[ 0, 0, 1, 0 ]21096
23[ 1, 0, 0, 0 ]8024
17[ 0, 0, 0, 1 ]32824
1[ 0, 0, 0, 0 ]1281

Highest weight: [ 0, 1, 1, 1 ]
Characteristic: 2
Dimension: 1007616

Level   dominant weight   weight multiplicity   length of W-orbit 
89[ 0, 1, 1, 1 ]1576
85[ 1, 0, 1, 2 ]2576
85[ 0, 2, 0, 0 ]296
83[ 1, 0, 2, 0 ]4288
81[ 1, 1, 0, 1 ]6576
79[ 0, 0, 1, 3 ]5192
77[ 2, 0, 0, 2 ]8144
77[ 0, 0, 2, 1 ]14192
75[ 2, 0, 1, 0 ]12288
75[ 0, 1, 0, 2 ]20288
73[ 0, 1, 1, 0 ]30288
71[ 1, 0, 0, 3 ]28144
69[ 1, 0, 1, 1 ]58576
67[ 3, 0, 0, 0 ]1624
65[ 1, 1, 0, 0 ]80192
65[ 0, 0, 0, 4 ]4024
63[ 0, 0, 1, 2 ]111192
61[ 2, 0, 0, 1 ]108144
61[ 0, 0, 2, 0 ]15296
59[ 0, 1, 0, 1 ]204288
55[ 1, 0, 0, 2 ]272144
53[ 1, 0, 1, 0 ]360288
49[ 0, 0, 0, 3 ]36024
47[ 0, 0, 1, 1 ]618192
45[ 2, 0, 0, 0 ]47224
43[ 0, 1, 0, 0 ]80096
39[ 1, 0, 0, 1 ]1028144
33[ 0, 0, 0, 2 ]131224
31[ 0, 0, 1, 0 ]166496
23[ 1, 0, 0, 0 ]209624
17[ 0, 0, 0, 1 ]262424
1[ 0, 0, 0, 0 ]32641

Highest weight: [ 1, 1, 1, 0 ]
Characteristic: 2
Dimension: 1007616

Level   dominant weight   weight multiplicity   length of W-orbit 
95[ 1, 1, 1, 0 ]1576
91[ 2, 0, 1, 1 ]2576
91[ 0, 0, 3, 0 ]296
89[ 0, 1, 1, 1 ]4576
87[ 2, 1, 0, 0 ]2192
85[ 1, 0, 1, 2 ]8576
85[ 0, 2, 0, 0 ]496
83[ 3, 0, 0, 1 ]4144
83[ 1, 0, 2, 0 ]8288
81[ 1, 1, 0, 1 ]15576
79[ 0, 0, 1, 3 ]14192
77[ 2, 0, 0, 2 ]16144
77[ 0, 0, 2, 1 ]26192
75[ 2, 0, 1, 0 ]30288
75[ 0, 1, 0, 2 ]28288
73[ 0, 1, 1, 0 ]52288
71[ 1, 0, 0, 3 ]44144
69[ 1, 0, 1, 1 ]88576
67[ 3, 0, 0, 0 ]3224
65[ 1, 1, 0, 0 ]94192
65[ 0, 0, 0, 4 ]4824
63[ 0, 0, 1, 2 ]146192
61[ 2, 0, 0, 1 ]148144
61[ 0, 0, 2, 0 ]15696
59[ 0, 1, 0, 1 ]238288
55[ 1, 0, 0, 2 ]256144
53[ 1, 0, 1, 0 ]388288
49[ 0, 0, 0, 3 ]37624
47[ 0, 0, 1, 1 ]608192
45[ 2, 0, 0, 0 ]41624
43[ 0, 1, 0, 0 ]65296
39[ 1, 0, 0, 1 ]940144
33[ 0, 0, 0, 2 ]100824
31[ 0, 0, 1, 0 ]143496
23[ 1, 0, 0, 0 ]153624
17[ 0, 0, 0, 1 ]215224
1[ 0, 0, 0, 0 ]23041

Highest weight: [ 1, 1, 1, 1 ]
Characteristic: 2
Dimension: 16777216

Level   dominant weight   weight multiplicity   length of W-orbit 
111[ 1, 1, 1, 1 ]11152
107[ 2, 0, 1, 2 ]2576
107[ 1, 2, 0, 0 ]2192
107[ 0, 0, 3, 1 ]2192
105[ 2, 0, 2, 0 ]4288
105[ 0, 1, 1, 2 ]4576
103[ 2, 1, 0, 1 ]6576
103[ 0, 1, 2, 0 ]8288
101[ 1, 0, 1, 3 ]8576
101[ 0, 2, 0, 1 ]12288
99[ 3, 0, 0, 2 ]8144
99[ 1, 0, 2, 1 ]22576
97[ 3, 0, 1, 0 ]12288
97[ 1, 1, 0, 2 ]30576
95[ 1, 1, 1, 0 ]44576
95[ 0, 0, 1, 4 ]14192
93[ 2, 0, 0, 3 ]40144
93[ 0, 0, 2, 2 ]52192
91[ 2, 0, 1, 1 ]80576
91[ 0, 1, 0, 3 ]68288
91[ 0, 0, 3, 0 ]7696
89[ 4, 0, 0, 0 ]1624
89[ 0, 1, 1, 1 ]136576
87[ 2, 1, 0, 0 ]108192
87[ 1, 0, 0, 4 ]88144
85[ 1, 0, 1, 2 ]228576
85[ 0, 2, 0, 0 ]18496
83[ 3, 0, 0, 1 ]144144
83[ 1, 0, 2, 0 ]308288
81[ 1, 1, 0, 1 ]400576
81[ 0, 0, 0, 5 ]11224
79[ 0, 0, 1, 3 ]370192
77[ 2, 0, 0, 2 ]512144
77[ 0, 0, 2, 1 ]644192
75[ 2, 0, 1, 0 ]664288
75[ 0, 1, 0, 2 ]816288
73[ 0, 1, 1, 0 ]1052288
71[ 1, 0, 0, 3 ]1024144
69[ 1, 0, 1, 1 ]1664576
67[ 3, 0, 0, 0 ]84824
65[ 1, 1, 0, 0 ]2094192
65[ 0, 0, 0, 4 ]128024
63[ 0, 0, 1, 2 ]2572192
61[ 2, 0, 0, 1 ]2616144
61[ 0, 0, 2, 0 ]322496
59[ 0, 1, 0, 1 ]3992288
55[ 1, 0, 0, 2 ]4920144
53[ 1, 0, 1, 0 ]6072288
49[ 0, 0, 0, 3 ]603224
47[ 0, 0, 1, 1 ]9086192
45[ 2, 0, 0, 0 ]745624
43[ 0, 1, 0, 0 ]1108896
39[ 1, 0, 0, 1 ]13480144
33[ 0, 0, 0, 2 ]1633624
31[ 0, 0, 1, 0 ]1976496
23[ 1, 0, 0, 0 ]2384024
17[ 0, 0, 0, 1 ]2868824
1[ 0, 0, 0, 0 ]344321