Frank Lübeck   

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Elementary Divisors for Partitions of n = 9

PartitionSpecht degreeelementary 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] 

Known Jantzen Filtrations

PartitionPrime 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

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