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Elementary Divisors for Partitions of n = 18

Partition	Specht degree	elementary divisors
(23,112)	663	[212*36*52*7*11] [215*36*52*7*11]15 [215*37*52*7*11] [215*37*53*7*11]102 [216*37*53*7*11]16 [216*37*53*72*11]528
(24,110)	2244	[212*36*52*7] [212*36*53*7]16 [212*36*53*72]118 [212*36*53*72*13]409 [213*36*53*72*13]103 [213*37*53*72*13]15 [214*37*53*72*13]1582
(25,18)	5508	[212*34*52*7] [212*34*52*72]16 [212*34*52*72*13]101 [213*34*52*72*13]545 [213*34*52*72*11*13]1037 [214*34*52*72*11*13]543 [214*34*53*72*11*13]3265
(26,16)	9996	[211*35*52] [211*35*52*13]134 [211*35*52*11*13]511 [211*35*53*11*13]951 [211*36*53*11*13]647 [211*37*53*11*13]1564 [212*37*53*11*13]1582 [213*37*53*11*13]118 [214*37*53*11*13]4488
(29)	4862	[212*36*52*7]16 [212*37*52*7]102 [213*37*52*7]410 [213*37*52*72]2737 [213*37*53*72]1341 [214*37*53*72]255 [214*38*53*72]
(3,2,113)	1344	[210*35*52*7*11*13]16 [210*36*52*7*11*13]118 [210*36*52*7*11*13*17]2 [210*36*53*7*11*13*17]648 [210*37*53*7*11*13*17]560
(3,22,111)	6885	[210*34*52*7*11]136 [210*34*52*72*11]408 [211*34*52*72*11]118 [214*34*52*72*11]682 [214*34*52*72*11*13]901 [215*34*52*72*11*13]118 [216*34*52*72*11*13]4522
(32,112)	4641	[211*35*52*7*11]118 [214*35*52*7*11] [215*35*52*7*11]529 [215*36*52*7*11]560 [215*36*53*7*11]1613 [215*37*53*7*11]1820
(4,2,112)	7020	[210*35*52*7*11]118 [211*35*52*7*11]562 [211*35*52*72*11]530 [211*35*52*72*11*17]3430 [212*35*52*72*11*17]562 [213*35*52*72*11*17]1818
(92)	4862	[2] [2*3]255 [22*3]1341 [22*3*5]2737 [22*3*5*7]410 [23*3*5*7]102 [23*32*5*7]16
(12,6)	9996	[1]4488 [2]118 [22]1582 [23]1564 [23*3]647 [23*32]951 [23*32*5]511 [23*32*5*11]134 [23*32*5*11*13]
(13,5)	5508	[1]3265 [5]543 [2*5]1037 [2*5*11]545 [22*5*11]101 [22*5*11*13]16 [22*5*7*11*13]
(14,2,12)	7020	[2]1818 [22]562 [23]3430 [23*17]530 [23*7*17]562 [24*7*17]118
(14,22)	4641	[2]1820 [2*3]1613 [2*3*5]560 [2*32*5]529 [22*32*5] [25*32*5]118
(14,3,1)	6885	[1]4522 [2]118 [22]901 [22*13]682 [25*13]118 [26*13]408 [26*7*13]136
(14,4)	2244	[1]1582 [2]15 [2*3]103 [22*3]409 [22*3*13]118 [22*3*7*13]16 [22*3*5*7*13]
(15,2,1)	1344	[1]560 [3]648 [3*5]2 [3*5*17]118 [32*5*17]16
(15,3)	663	[1]528 [7]16 [2*7]102 [2*5*7] [2*3*5*7]15 [24*3*5*7]

Known Jantzen Filtrations

Partition	Prime	Jantzen Filtration
(2,116)	5	[D(5,43,1)]3
(2,116)	11	[D(27,14)]1
(2,116)	13	[D(25,18)]1
(22,114)	5	[D(44,12)]2
(22,114)	11	[D(26,16)]1
(22,114)	13	[D(24,110)]1
(22,114)	17	[D(22,114)]0 +[D(3,2,113)]1
(23,112)	5	[D(5,43,1)]2 +[D(43,3,13)]3
(23,112)	11	[D(25,18)]1
(24,110)	5	[D(52,42)]2 +[D(42,32,14)]3
(24,110)	13	[D(24,110)]0 +[D(33,2,17)]1
(25,18)	5	[D(42,32,14)]2 +[D(4,33,2,13)]3
(25,18)	11	[D(25,18)]0 +[D(34,2,14)]1
(25,18)	13	[D(25,18)]0 +[D(32,23,16)]1
(29)	5	[D(4,33,2,13)]2 +[D(63)]3
(3,115)	5	[D(44,2)]3
(3,115)	11	[D(3,25,15)]1
(3,115)	13	[D(3,23,19)]1
(3,2,113)	5	[D(44,2)]2 +[D(43,3,2,1)]3
(3,2,113)	11	[D(3,24,17)]1
(3,2,113)	13	[D(3,22,111)]1
(3,2,113)	17	[D(3,2,113)]0 +[D(4,2,112)]1
(32,112)	5	[D(43,3,2,1)]2 +[D(42,32,22)]3
(32,112)	11	[D(32,22,18)]1
(4,114)	5	[D(43,32)]2
(4,114)	11	[D(4,24,16)]1
(4,114)	13	[D(4,22,110)]1
(5,113)	5	[D(5,4,33)]2
(5,113)	11	[D(5,23,17)]1
(5,113)	13	[D(5,2,111)]1
(92)	5	[D(92)]0 +[D(13,5)]1
(13,5)	5	[D(13,5)]0 +[D(14,4)]1
(13,5)	11	[D(13,5)]0 +[D(15,3)]1
(13,5)	13	[D(13,5)]0 +[D(17,1)]1
(14,22)	5	[D(14,22)]0 +[D(15,2,1)]1
(14,4)	5	[D(14,4)]0 +[D(18)]1
(14,4)	13	[D(14,4)]0 +[D(16,2)]1
(15,2,1)	5	[D(15,2,1)]0 +[D(16,12)]1
(15,2,1)	17	[D(15,2,1)]0 +[D(16,2)]1
(15,3)	5	[D(15,3)]0 +[D(17,1)]1
(16,2)	17	[D(16,2)]0 +[D(18)]1

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