Partition | Specht degree | elementary divisors |
(23,13) | 48 | [23*32] [23*32*7]6 [23*33*7]20 [23*33*5*7]21 |
(24,1) | 42 | [25*32]8 [25*32*5]18 [26*32*5]15 [26*33*5] |
(3,2,14) | 105 | [23*3]7 [23*32]19 [25*32] [27*32]43 [27*33]35 |
(3,22,12) | 162 | [23]26 [24]2 [24*5]19 [24*5*7]73 [25*5*7]2 [26*5*7]40 |
(3,23) | 84 | [22*3] [22*3*5]25 [23*3*5]15 [23*32*5]3 [24*32*5]33 [24*33*5]7 |
(32,13) | 120 | [22*3]19 [22*3*7]23 [22*32*7]36 [23*32*7]7 [23*33*7]35 |
(32,2,1) | 168 | [23]8 [24]33 [24*3]43 [24*32]50 [24*32*5]13 [24*33*5]21 |
(33) | 42 | [23*3]21 [23*32*5]21 |
(4,2,13) | 189 | [2*3]56 [2*3*5]22 [23*3*5] [24*3*5]40 [25*3*5]2 [26*3*5]68 |
(4,22,1) | 216 | [22]56 [23]27 [23*5]32 [23*5*7]74 [23*3*5*7]27 |
(4,3,12) | 216 | [2]27 [2*3]74 [2*3*7]32 [2*3*5*7]27 [22*3*5*7]56 |
(4,3,2) | 168 | [1]21 [3]13 [3*5]50 [32*5]43 [33*5]33 [2*33*5]8 |
(42,1) | 84 | [2]7 [2*3]33 [22*3]3 [22*32]15 [23*32]25 [23*32*5] |
(5,2,12) | 189 | [2]68 [22]2 [23]40 [24] [26]22 [26*5]56 |
(5,22) | 120 | [2]35 [2*3]7 [22*3]36 [22*32]23 [22*32*7]19 |
(5,3,1) | 162 | [1]40 [2]2 [22]73 [22*7]19 [22*5*7]2 [23*5*7]26 |
(5,4) | 42 | [1] [3]15 [2*3]18 [2*3*5]8 |
(6,2,1) | 105 | [1]35 [3]43 [22*3] [24*3]19 [24*32]7 |
(6,3) | 48 | [1]21 [5]20 [3*5]6 [3*5*7] |
Partition | Prime |
Jantzen Filtration |
(19) | 2 |
[D(9)]7
|
(19) | 3 |
[D(5,4)]4
|
(19) | 5 |
[D(3,23)]1
|
(19) | 7 |
[D(23,13)]1
|
(2,17) | 2 |
[D(8,1)]4
|
(2,17) | 3 |
[D(5,4)]2
+[D(42,1)]4
|
(2,17) | 5 |
[D(24,1)]1
|
(2,17) | 7 |
[D(22,15)]1
|
(22,15) | 2 |
[D(9)]5
+[D(7,2)]7
|
(22,15) | 3 |
[D(4,3,12)]1
|
(22,15) | 5 |
[D(23,13)]1
|
(22,15) | 7 |
[D(22,15)]0
+[D(32,13)]1
|
(23,13) | 2 |
[D(6,3)]3
|
(23,13) | 3 |
[D(42,1)]2
+[D(32,2,1)]3
|
(23,13) | 5 |
[D(23,13)]0
+[D(33)]1
|
(23,13) | 7 |
[D(23,13)]0
+[D(3,22,12)]1
|
(24,1) | 2 |
[D(7,2)]5
+[D(5,4)]6
|
(24,1) | 3 |
[D(32,2,1)]2
+[D(9)]3
|
(24,1) | 5 |
[D(24,1)]0
+[D(4,3,2)]1
|
(3,16) | 2 |
[D(7,2)+2*D(9)]4
|
(3,16) | 3 |
[D(42,1)]2
+[D(4,3,2)]4
|
(3,16) | 5 |
[D(3,22,12)]1
|
(3,2,14) | 2 |
[D(7,2)]3
+[D(9)]5
+[D(6,2,1)]7
|
(3,2,14) | 3 |
[D(42,1)]1
+[D(32,2,1)+D(4,3,2)+D(5,4)]2
+[D(5,22)]3
|
(3,22,12) | 2 |
[D(7,2)]3
+[D(5,4)+D(6,2,1)]4
+[2*D(9)]5
+[D(5,3,1)]6
|
(3,22,12) | 5 |
[D(3,22,12)]0
+[D(32,2,1)]1
|
(3,22,12) | 7 |
[D(3,22,12)]0
+[D(4,22,1)]1
|
(3,23) | 2 |
[D(7,2)]2
+[D(5,4)+2*D(9)]3
+[D(5,3,1)]4
|
(3,23) | 3 |
[D(32,2,1)]1
+[D(5,22)+D(9)]2
+[D(8,1)]3
|
(3,23) | 5 |
[D(3,23)]0
+[D(4,22,1)]1
|
(32,13) | 2 |
[D(6,2,1)]2
+[D(5,3,1)+2*D(9)]3
|
(32,13) | 7 |
[D(32,13)]0
+[D(4,3,12)]1
|
(32,2,1) | 2 |
[D(8,1)]3
+[D(4,3,2)]4
|
(32,2,1) | 5 |
[D(32,2,1)]0
+[D(5,4)]1
|
(33) | 2 |
[D(5,3,1)+2*D(9)]3
|
(33) | 5 |
[D(33)]0
+[D(6,3)]1
|
(4,15) | 2 |
[D(6,3)+D(8,1)]3
|
(4,15) | 3 |
[D(4,3,2)]1
+[D(5,22)]3
|
(4,15) | 5 |
[D(4,2,13)]1
|
(4,2,13) | 2 |
[D(6,2,1)]1
+[D(9)]3
+[D(5,3,1)]4
+[2*D(9)]5
+[D(5,4)+2*D(7,2)]6
|
(4,2,13) | 3 |
[D(4,22,1)]1
|
(4,2,13) | 5 |
[D(4,2,13)]0
+[D(4,3,12)]1
|
(4,22,1) | 2 |
[D(6,3)+D(8,1)]2
+[D(4,3,2)]3
|
(4,22,1) | 3 |
[D(4,22,1)]0
+[D(7,2)]1
|
(4,22,1) | 5 |
[D(4,22,1)]0
+[D(5,2,12)]1
|
(4,22,1) | 7 |
[D(4,22,1)]0
+[D(5,22)]1
|
(4,3,12) | 2 |
[D(4,3,2)]1
+[D(6,3)+D(8,1)]2
|
(4,3,12) | 3 |
[D(4,3,12)]0
+[D(5,2,12)]1
|
(4,3,12) | 5 |
[D(4,3,12)]0
+[D(42,1)]1
|
(4,3,12) | 7 |
[D(4,3,12)]0
+[D(5,3,1)]1
|
(4,3,2) | 2 |
[D(4,3,2)]0
+[D(8,1)]1
|
(4,3,2) | 5 |
[D(4,3,2)]0
+[D(5,3,1)]1
|
(42,1) | 2 |
[D(5,3,1)]1
+[D(5,4)+2*D(9)]2
+[D(7,2)]3
|
(42,1) | 3 |
[D(42,1)]0
+[D(5,4)+D(6,2,1)]1
+[D(6,3)]2
|
(42,1) | 5 |
[D(42,1)]0
+[D(9)]1
|
(5,14) | 2 |
[D(5,4)+2*D(7,2)+2*D(9)]3
|
(5,2,12) | 2 |
[D(5,4)+2*D(7,2)]1
+[2*D(9)]2
+[D(5,3,1)]3
+[D(9)]4
+[D(6,2,1)]6
|
(5,2,12) | 5 |
[D(5,2,12)]0
+[D(6,13)]1
|
(5,22) | 2 |
[D(5,3,1)+2*D(9)]1
+[D(6,2,1)]2
|
(5,22) | 7 |
[D(5,22)]0
+[D(7,2)]1
|
(5,3,1) | 2 |
[D(5,3,1)]0
+[2*D(9)]1
+[D(5,4)+D(6,2,1)]2
+[D(7,2)]3
|
(5,3,1) | 5 |
[D(5,3,1)]0
+[D(7,12)]1
|
(5,3,1) | 7 |
[D(5,3,1)]0
+[D(6,3)]1
|
(5,4) | 2 |
[D(5,4)]0
+[D(7,2)]1
|
(5,4) | 3 |
[D(5,4)]0
+[D(6,3)]1
|
(5,4) | 5 |
[D(5,4)]0
+[D(8,1)]1
|
(6,13) | 2 |
[D(6,3)+D(8,1)]1
|
(6,13) | 3 |
[D(6,2,1)]1
+[D(7,12)]3
|
(6,2,1) | 2 |
[D(6,2,1)]0
+[D(9)]2
+[D(7,2)]4
|
(6,2,1) | 3 |
[D(6,2,1)]0
+[D(6,3)+D(7,12)+D(9)]1
+[D(8,1)]2
|
(6,3) | 3 |
[D(6,3)]0
+[D(8,1)]1
|
(6,3) | 5 |
[D(6,3)]0
+[D(7,2)]1
|
(6,3) | 7 |
[D(6,3)]0
+[D(9)]1
|
(7,12) | 2 |
[D(7,2)+2*D(9)]1
|
(7,12) | 3 |
[D(7,12)]0
+[D(8,1)]2
|
(7,2) | 2 |
[D(7,2)]0
+[D(9)]2
|
(7,2) | 7 |
[D(7,2)]0
+[D(8,1)]1
|
(8,1) | 3 |
[D(8,1)]0
+[D(9)]2
|