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Elementary Divisors for Partitions of n = 7

Partition	Specht degree	elementary divisors
(23,1)	14	[22*3] [22*3*5]5 [23*3*5]7 [23*32*5]
(3,2,12)	35	[2]13 [2*3] [23*3] [24*32]20
(3,22)	21	[22] [23]12 [23*5]2 [23*3*5]6
(32,1)	21	[2]6 [2*3]2 [2*3*5]12 [22*3*5]
(4,2,1)	35	[1]20 [2*3] [23*3] [23*32]13
(4,3)	14	[1] [3]7 [2*3]5 [2*3*5]

Known Jantzen Filtrations

Partition	Prime	Jantzen Filtration
(17)	2	[D(7)]4
(17)	3	[D(4,3)]2
(17)	5	[D(23,1)]1
(17)	7	[D(2,15)]1
(2,15)	2	[D(6,1)]3
(2,15)	3	[D(32,1)]1
(2,15)	5	[D(22,13)]1
(2,15)	7	[D(2,15)]0 +[D(3,14)]1
(22,13)	2	[D(5,2)]3
(22,13)	3	[D(4,3)]1 +[D(3,2,12)]2
(22,13)	5	[D(22,13)]0 +[D(32,1)]1
(23,1)	2	[D(6,1)]2 +[D(4,3)]3
(23,1)	3	[D(3,2,12)]1 +[D(7)]2
(23,1)	5	[D(23,1)]0 +[D(3,22)]1
(3,14)	2	[D(5,2)+D(7)]3
(3,14)	3	[D(3,22)]1
(3,14)	7	[D(3,14)]0 +[D(4,13)]1
(3,2,12)	2	[D(5,2)]1 +[D(7)]3 +[D(4,2,1)]4
(3,2,12)	3	[D(3,2,12)]0 +[D(4,3)+D(7)]1 +[D(4,2,1)]2
(3,22)	2	[D(7)]2 +[D(4,2,1)]3
(3,22)	3	[D(3,22)]0 +[D(6,1)]1
(3,22)	5	[D(3,22)]0 +[D(5,2)]1
(32,1)	2	[D(4,2,1)]1 +[D(7)]2
(32,1)	3	[D(32,1)]0 +[D(5,12)]1
(32,1)	5	[D(32,1)]0 +[D(4,3)]1
(4,13)	2	[D(4,3)+2*D(6,1)]1
(4,13)	3	[D(4,2,1)]1
(4,13)	7	[D(4,13)]0 +[D(5,12)]1
(4,2,1)	2	[D(4,2,1)]0 +[D(7)]1 +[D(5,2)]3
(4,2,1)	3	[D(4,2,1)]0 +[D(4,3)+D(7)]1 +[D(5,2)]2
(4,3)	2	[D(4,3)]0 +[D(6,1)]1
(4,3)	3	[D(4,3)]0 +[D(5,2)]1
(4,3)	5	[D(4,3)]0 +[D(7)]1
(5,12)	2	[D(5,2)+D(7)]1
(5,12)	7	[D(5,12)]0 +[D(6,1)]1
(5,2)	3	[D(5,2)]0 +[D(7)]1
(5,2)	5	[D(5,2)]0 +[D(6,1)]1
(6,1)	7	[D(6,1)]0 +[D(7)]1

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