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Elementary Divisors for Partitions of n = 16

Partition	Specht degree	elementary divisors
(23,110)	440	[210*35*52*7] [210*35*52*72]14 [210*35*52*72*13]75 [211*35*52*72*13]13 [211*36*52*72*13] [212*36*52*72*13]336
(24,18)	1260	[211*34*5*7] [211*34*5*7*13]13 [212*34*5*7*13]90 [212*34*5*7*11*13]246 [213*34*5*7*11*13]90 [213*34*52*7*11*13]820
(25,16)	2548	[210*34*52]15 [210*34*52*11]88 [210*34*53*11]234 [210*35*53*11]103 [210*36*53*11]470 [211*36*53*11]336 [212*36*53*11]14 [213*36*53*11]1288
(26,14)	3640	[29*34*52] [29*34*52*11]102 [29*35*52*11]233 [210*35*52*11]14 [211*35*52*11]910 [211*35*52*7*11]468 [212*35*52*7*11]484 [212*36*52*7*11]1428
(27,12)	3432	[29*34*52*7]15 [29*35*52*7]75 [210*35*52*7]349 [210*35*52*72]1577 [211*35*52*72]429 [211*35*53*72]859 [212*35*53*72]128
(28)	1430	[211*34*5*7] [211*35*5*7]13 [212*35*5*7]75 [212*35*5*72]731 [212*35*52*72]482 [213*35*52*72]127 [213*36*52*72]
(3,2,111)	896	[28*34*52*7*11]103 [28*35*53*7*11]2 [28*35*53*7*11*13]336 [28*36*53*7*11*13]455
(3,22,19)	3900	[29*34*5*7]14 [210*34*5*7]91 [210*35*5*7]245 [211*35*5*7]89 [211*35*5*72]457 [211*35*5*72*11]454 [212*35*5*72*11]2 [213*35*5*72*11]2548
(3,23,17)	10752	[26*33*5*7]103 [26*33*52*7]2 [26*33*52*7*11]1154 [26*33*52*7*11*13]2083 [26*33*53*7*11*13]453 [26*34*53*7*11*13]105 [26*35*53*7*11*13]6852
(32,110)	2640	[29*34*52*7]89 [29*34*52*72] [210*34*52*72]701 [210*34*52*72*13]484 [210*35*52*72*13]1365
(4,2,110)	4004	[28*34*52*7]90 [210*34*52*7]365 [210*35*52*7]338 [210*36*53*7]2211 [212*36*53*7]1000
(5,2,19)	11648	[27*34*5*7]1365 [27*34*5*7*11]1846 [27*35*52*7*11]5434 [27*35*53*7*11]3003
(82)	1430	[2] [2*3]127 [22*3]482 [22*3*5]731 [22*3*5*7]75 [23*3*5*7]13 [23*32*5*7]
(9,7)	3432	[1]128 [2]859 [2*5]429 [22*5]1577 [22*5*7]349 [23*5*7]75 [23*3*5*7]15
(10,6)	3640	[1]1428 [3]484 [2*3]468 [2*3*7]910 [22*3*7]14 [23*3*7]233 [23*32*7]102 [23*32*7*11]
(11,2,13)	11648	[2*3]3003 [2*3*5]5434 [2*32*52]1846 [2*32*52*11]1365
(11,4,1)	10752	[1]6852 [3]105 [32]453 [32*5]2083 [32*5*13]1154 [32*5*11*13]2 [32*52*11*13]103
(11,5)	2548	[1]1288 [2]14 [22]336 [23]470 [23*3]103 [23*32]234 [23*32*5]88 [23*32*5*11]15
(12,2,12)	4004	[2]1000 [23]2211 [23*3*5]338 [23*32*5]365 [25*32*5]90
(12,22)	2640	[2]1365 [2*3]484 [2*3*13]701 [22*3*13] [22*3*7*13]89
(12,3,1)	3900	[1]2548 [2]2 [22]454 [22*11]457 [22*7*11]89 [23*7*11]245 [23*3*7*11]91 [24*3*7*11]14
(12,4)	1260	[1]820 [5]90 [2*5]246 [2*5*11]90 [22*5*11]13 [22*5*11*13]
(13,2,1)	896	[1]455 [3]336 [3*13]2 [32*5*13]103
(13,3)	440	[1]336 [2] [2*3]13 [22*3]75 [22*3*13]14 [22*3*7*13]

Known Jantzen Filtrations

Partition	Prime	Jantzen Filtration
(2,114)	5	[D(43,3,1)]2
(2,114)	11	[D(25,16)]1
(2,114)	13	[D(23,110)]1
(22,112)	5	[D(44)]2 +[D(42,32,12)]3
(22,112)	11	[D(24,18)]1
(23,110)	5	[D(4,33,13)]2
(23,110)	13	[D(23,110)]0 +[D(32,2,18)]1
(24,18)	5	[D(4,33,13)]1 +[D(34,14)]2
(24,18)	11	[D(24,18)]0 +[D(33,2,15)]1
(24,18)	13	[D(24,18)]0 +[D(3,23,17)]1
(25,16)	5	[D(42,32,12)]2 +[D(33,22,13)]3
(25,16)	11	[D(25,16)]0 +[D(32,23,14)]1
(26,14)	5	[D(32,24,12)]2
(26,14)	11	[D(26,14)]0 +[D(3,25,13)]1
(27,12)	5	[D(33,22,13)]2 +[D(6,52)]3
(28)	5	[D(34,14)]1 +[D(62,4)]2
(3,113)	5	[D(42,32,2)]2
(3,113)	11	[D(3,23,17)]1
(3,113)	13	[D(3,2,111)]1
(3,2,111)	5	[D(42,32,12)]2 +[D(4,33,2,1)]3
(3,2,111)	11	[D(3,22,19)]1
(3,2,111)	13	[D(3,2,111)]0 +[D(32,110)]1
(3,22,19)	5	[D(34,2,12)]1
(3,22,19)	11	[D(3,22,19)]0 +[D(33,17)]1
(32,110)	5	[D(34,22)]2
(32,110)	13	[D(32,110)]0 +[D(42,18)]1
(4,112)	5	[D(4,34)]2
(4,112)	11	[D(4,22,18)]1
(4,2,110)	5	[D(4,33,2,1)]2 +[D(5,32,22,1)]3
(5,111)	5	[D(5,33,2)]2
(5,111)	11	[D(5,2,19)]1
(6,110)	5	[D(6,32,22)]2
(82)	5	[D(82)]0 +[D(12,4)]1
(9,7)	5	[D(9,7)]0 +[D(11,5)]1
(10,6)	11	[D(10,6)]0 +[D(16)]1
(11,15)	5	[D(11,2,13)]1
(11,5)	5	[D(11,5)]0 +[D(14,2)]1
(11,5)	11	[D(11,5)]0 +[D(15,1)]1
(12,2,12)	5	[D(12,2,12)]0 +[D(13,2,1)]1
(12,22)	13	[D(12,22)]0 +[D(13,2,1)]1
(12,3,1)	11	[D(12,3,1)]0 +[D(13,2,1)]1
(12,4)	5	[D(12,4)]0 +[D(13,3)]1
(12,4)	11	[D(12,4)]0 +[D(14,2)]1
(12,4)	13	[D(12,4)]0 +[D(16)]1
(13,2,1)	5	[D(13,2,1)]0 +[D(14,2)]1
(13,2,1)	13	[D(13,2,1)]0 +[D(14,12)]1
(13,3)	13	[D(13,3)]0 +[D(15,1)]1
(14,2)	5	[D(14,2)]0 +[D(16)]1

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