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Elementary Divisors for Partitions of n = 8

Partition	Specht degree	elementary divisors
(23,12)	28	[23*32]7 [23*32*5]7 [24*32*5]6 [25*32*5]8
(24)	14	[24*3] [24*3*5]5 [25*3*5]7 [25*32*5]
(3,2,13)	64	[2*3]19 [2*3*7]2 [2*3*5*7]8 [2*32*5*7]35
(3,22,1)	70	[22]6 [23]8 [24]14 [25*3]2 [26*3]33 [26*32]7
(32,12)	56	[22]13 [22*3] [23*3]7 [23*32]22 [23*32*5]13
(32,2)	42	[23]21 [23*3*5]21
(4,2,12)	90	[2]14 [23]31 [23*7]31 [25*7]14
(4,22)	56	[2]13 [2*5]22 [2*3*5]7 [22*3*5] [22*32*5]13
(4,3,1)	70	[1]7 [3]33 [2*3]2 [22*32]14 [23*32]8 [24*32]6
(42)	14	[2] [2*3]7 [22*3]5 [22*3*5]
(5,2,1)	64	[1]35 [3]8 [3*5]2 [3*5*7]19
(5,3)	28	[1]8 [2]6 [22]7 [22*5]7

Known Jantzen Filtrations

Partition	Prime	Jantzen Filtration
(18)	2	[D(8)]7
(18)	3	[D(42)]2
(18)	5	[D(24)]1
(18)	7	[D(22,14)]1
(2,16)	2	[D(8)]4 +[D(7,1)]7
(2,16)	3	[D(4,3,1)]2
(2,16)	5	[D(23,12)]1
(22,14)	2	[D(7,1)]4 +[D(6,2)]5
(22,14)	3	[D(4,3,1)]1 +[D(32,12)]2
(22,14)	7	[D(22,14)]0 +[D(3,2,13)]1
(23,12)	2	[D(6,2)]3 +[D(7,1)]4 +[D(5,3)]5
(23,12)	3	[D(3,22,1)]2
(23,12)	5	[D(23,12)]0 +[D(32,2)]1
(24)	2	[D(7,1)]4 +[D(5,3)]5
(24)	3	[D(32,12)]1 +[D(8)]2
(24)	5	[D(24)]0 +[D(4,22)]1
(3,15)	2	[D(7,1)]3 +[D(6,2)+D(8)]6
(3,15)	3	[D(32,2)]1
(3,15)	5	[D(3,2,13)]1
(3,2,13)	2	[D(5,2,1)]1
(3,2,13)	3	[D(3,22,1)+D(42)]1 +[D(4,22)]2
(3,2,13)	5	[D(3,2,13)]0 +[D(32,12)]1
(3,2,13)	7	[D(3,2,13)]0 +[D(4,2,12)]1
(3,22,1)	2	[D(7,1)]2 +[D(5,3)]3 +[D(6,2)]4 +[2*D(8)]5 +[D(4,3,1)]6
(3,22,1)	3	[D(3,22,1)]0 +[D(4,22)]1 +[D(7,1)]2
(32,12)	2	[D(6,2)]2 +[D(4,3,1)+2*D(8)]3
(32,12)	3	[D(32,12)]0 +[D(4,3,1)+D(8)]1 +[D(5,2,1)]2
(32,12)	5	[D(32,12)]0 +[D(42)]1
(32,2)	2	[D(4,3,1)+2*D(8)]3
(32,2)	3	[D(32,2)]0 +[D(6,12)]1
(32,2)	5	[D(32,2)]0 +[D(5,3)]1
(4,14)	3	[D(4,22)]1
(4,2,12)	7	[D(4,2,12)]0 +[D(5,2,1)]1
(4,22)	2	[D(4,3,1)+2*D(8)]1 +[D(6,2)]2
(4,22)	3	[D(4,22)]0 +[D(42)+D(7,1)]1 +[D(6,2)]2
(4,22)	5	[D(4,22)]0 +[D(5,2,1)]1
(4,3,1)	2	[D(4,3,1)]0 +[2*D(8)]1 +[D(6,2)]2 +[D(5,3)]3 +[D(7,1)]4
(4,3,1)	3	[D(4,3,1)]0 +[D(5,2,1)]1 +[D(5,3)]2
(42)	2	[D(5,3)]1 +[D(7,1)]2
(42)	3	[D(42)]0 +[D(6,2)]1
(42)	5	[D(42)]0 +[D(8)]1
(5,13)	3	[D(5,2,1)]1
(5,2,1)	3	[D(5,2,1)]0 +[D(5,3)+D(8)]1
(5,2,1)	5	[D(5,2,1)]0 +[D(6,12)]1
(5,2,1)	7	[D(5,2,1)]0 +[D(6,2)]1
(5,3)	2	[D(5,3)]0 +[D(7,1)]1 +[D(6,2)]2
(5,3)	5	[D(5,3)]0 +[D(7,1)]1
(6,12)	2	[D(6,2)+D(8)]1 +[D(7,1)]4
(6,2)	2	[D(6,2)]0 +[D(7,1)]1
(6,2)	3	[D(6,2)]0 +[D(7,1)]1
(6,2)	7	[D(6,2)]0 +[D(8)]1
(7,1)	2	[D(7,1)]0 +[D(8)]3

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Last updated: Mon Jul 12 23:23:20 2004 (CET)