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Elementary Divisors for Partitions of n = 15

Partition	Specht degree	elementary divisors
(23,19)	350	[29*35*5*7] [29*35*5*7*13]12 [29*36*5*7*13] [210*36*5*7*13]76 [210*36*5*7*11*13]260
(24,17)	910	[210*34*5*7]14 [210*34*5*7*11]76 [210*34*52*7*11]247 [210*35*52*7*11]13 [210*36*52*7*11]560
(25,15)	1638	[28*33*52] [28*33*52*11]12 [28*33*53*11]77 [28*34*53*11]246 [29*34*53*11]14 [210*34*53*11]560 [210*34*53*7*11]728
(26,13)	2002	[29*34*52]13 [29*35*52]77 [210*35*52]260 [210*35*52*7]224 [210*36*52*7]1051 [210*36*53*7]377
(27,1)	1430	[28*34*5*7] [28*35*5*7]13 [29*35*5*7]75 [29*35*5*72]731 [29*35*52*72]482 [210*35*52*72]127 [210*36*52*72]
(3,2,110)	715	[28*34*52*7]13 [28*35*52*7]76 [28*35*52*72] [210*35*52*72] [211*35*52*72]338 [211*36*52*72]286
(3,22,18)	2835	[29*32*5*7]91 [29*32*5*7*11]258 [29*32*5*7*11*13]366 [29*32*52*7*11*13]196 [210*32*52*7*11*13]624 [211*32*52*7*11*13]1300
(3,23,16)	7007	[26*33*5]13 [26*33*52]324 [26*34*52]299 [26*35*52]274 [28*35*52]365 [28*36*52]442 [28*36*53]493 [29*36*53]624 [210*36*53] [211*36*53]4172
(3,24,14)	11375	[28*33]13 [28*34]611 [29*34]27 [29*35]64 [210*35]922 [210*35*11]1198 [210*35*7*11]3964 [211*35*7*11]1014 [211*36*7*11]3562
(3,25,12)	11583	[27*32*5]89 [27*32*5*7] [28*32*5*7]1535 [28*32*52*7]377 [29*32*52*7]55 [29*32*52*72]4522 [210*32*52*72]713 [210*32*53*72]3459 [211*32*53*72]832
(3,26)	5005	[28*33*5] [29*33*5]90 [29*33*5*7]1337 [29*34*5*7]2 [29*35*5*7]690 [29*35*52*7]2053 [210*35*52*7]819 [210*36*52*7]13
(32,19)	1925	[28*34*5*7]76 [28*34*5*7*13]262 [28*35*5*7*13]286 [29*35*5*7*13] [210*35*5*7*13]585 [210*36*5*7*13]715
(32,2,17)	9100	[27*32*5*7]336 [28*32*5*7] [28*33*5*7]872 [28*34*5*7]443 [29*34*5*7]273 [29*35*5*7]819 [29*35*5*7*11]5069 [29*36*5*7*11]1287
(35)	6006	[26*32*5]78 [26*32*52]650 [26*32*52*7]572 [27*32*52*7]2262 [27*33*52*7]1729 [27*34*52*7]338 [27*34*53*7]377
(4,2,19)	2925	[27*34*5*7]364 [27*34*5*7*11]260 [28*34*5*7*11]2 [28*34*5*72*11]1299 [210*34*5*72*11]1000
(4,22,17)	11088	[26*32*5*7]78 [26*32*52*7]2408 [26*32*52*7*13]439 [26*34*52*7*13]2729 [26*34*53*7*13]5434
(4,3,18)	9450	[27*32*5*7]1728 [27*33*5*7]121 [27*33*5*7*13]712 [27*33*5*7*11*13]4887 [28*33*5*7*11*13]2002
(5,2,18)	7722	[27*32*5*7]286 [27*32*52*7]714 [28*32*52*7]1299 [28*32*52*72] [29*32*52*72]4135 [29*32*53*72]1287
(53)	6006	[23*3]377 [23*3*5]338 [23*32*5]1729 [23*33*5]2262 [24*33*5]572 [24*33*5*7]650 [24*33*52*7]78
(72,1)	5005	[2]13 [2*3]819 [22*3]2053 [22*3*5]690 [22*32*5]2 [22*33*5]1337 [22*33*5*7]90 [23*33*5*7]
(8,6,1)	11583	[1]832 [2]3459 [2*5]713 [22*5]4522 [22*5*7]55 [23*5*7]377 [23*52*7]1535 [24*52*7] [24*52*72]89
(8,7)	1430	[1] [3]127 [2*3]482 [2*3*5]731 [2*3*5*7]75 [22*3*5*7]13 [22*32*5*7]
(9,5,1)	11375	[1]3562 [3]1014 [2*3]3964 [2*3*7]1198 [2*3*7*11]922 [22*3*7*11]64 [22*32*7*11]27 [23*32*7*11]611 [23*33*7*11]13
(9,6)	2002	[1]377 [5]1051 [3*5]224 [3*5*7]260 [2*3*5*7]77 [2*32*5*7]13
(10,2,13)	7722	[2*3]1287 [2*3*5]4135 [22*3*5] [22*3*5*7]1299 [23*3*5*7]714 [23*3*52*7]286
(10,22,1)	9450	[22]2002 [23]4887 [23*11]712 [23*11*13]121 [23*3*11*13]1728
(10,3,12)	11088	[2]5434 [2*5]2729 [2*32*5]439 [2*32*5*13]2408 [2*32*52*13]78
(10,3,2)	9100	[1]1287 [3]5069 [3*11]819 [32*11]273 [2*32*11]443 [2*33*11]872 [2*34*11] [22*34*11]336
(10,4,1)	7007	[1]4172 [2] [22]624 [23]493 [23*5]442 [23*3*5]365 [25*3*5]274 [25*32*5]299 [25*33*5]324 [25*33*52]13
(10,5)	1638	[1]728 [7]560 [2*7]14 [22*7]246 [22*3*7]77 [22*3*5*7]12 [22*3*5*7*11]
(11,2,12)	2925	[2]1000 [23]1299 [23*7]2 [24*7]260 [24*7*11]364
(11,22)	1925	[2]715 [2*3]585 [22*3] [23*3]286 [23*32]262 [23*32*13]76
(11,3,1)	2835	[1]1300 [2]624 [22]196 [22*5]366 [22*5*13]258 [22*5*11*13]91
(11,4)	910	[1]560 [3]13 [32]247 [32*5]76 [32*5*11]14
(12,2,1)	715	[1]286 [3]338 [2*3] [23*3] [23*3*7]76 [23*32*7]13
(12,3)	350	[1]260 [11]76 [2*11] [2*3*11]12 [2*3*11*13]

Known Jantzen Filtrations

Partition	Prime	Jantzen Filtration
(2,113)	5	[D(43,3)]2 +[D(42,32,1)]3
(2,113)	11	[D(24,17)]1
(2,113)	13	[D(22,111)]1
(22,111)	5	[D(4,33,12)]2
(22,111)	11	[D(23,19)]1
(22,111)	13	[D(22,111)]0 +[D(32,19)]1
(23,19)	5	[D(34,13)]1
(23,19)	11	[D(23,19)]0 +[D(33,16)]1
(23,19)	13	[D(23,19)]0 +[D(3,22,18)]1
(24,17)	5	[D(4,33,12)]1 +[D(33,2,14)]2
(24,17)	11	[D(24,17)]0 +[D(32,22,15)]1
(25,15)	5	[D(42,32,1)]2 +[D(32,23,13)]3
(25,15)	11	[D(25,15)]0 +[D(3,24,14)]1
(26,13)	5	[D(32,23,13)]2 +[D(53)]3
(27,1)	5	[D(33,2,14)]1 +[D(6,5,4)]2
(3,112)	5	[D(42,32,1)]2 +[D(4,33,2)]3
(3,112)	11	[D(3,22,18)]1
(3,2,110)	5	[D(34,2,1)]2
(3,22,18)	5	[D(34,2,1)]1 +[D(33,22,12)]2
(3,22,18)	11	[D(3,22,18)]0 +[D(32,2,17)]1
(3,22,18)	13	[D(3,22,18)]0 +[D(4,22,17)]1
(3,26)	5	[D(33,22,12)]1 +[D(6,42,1)]2
(32,19)	5	[D(33,23)]1
(32,19)	13	[D(32,19)]0 +[D(4,3,18)]1
(4,111)	5	[D(4,33,2)]2 +[D(5,32,22)]3
(4,111)	11	[D(4,2,19)]1
(4,2,19)	5	[D(4,32,22,1)]1
(4,2,19)	11	[D(4,2,19)]0 +[D(4,3,18)]1
(5,110)	5	[D(5,32,22)]2 +[D(6,3,23)]3
(6,19)	5	[D(6,3,23)]1 +[D(7,24)]2
(7,18)	5	[D(7,24)]1 +[D(8,23,1)]2
(72,1)	5	[D(72,1)]0 +[D(11,3,1)]1
(8,7)	5	[D(8,7)]0 +[D(11,4)]1
(9,16)	5	[D(9,22,12)]1 +[D(10,2,13)]2
(9,6)	5	[D(9,6)]0 +[D(10,5)]1
(10,15)	5	[D(10,2,13)]1 +[D(11,14)]2
(10,5)	5	[D(10,5)]0 +[D(14,1)]1
(10,5)	11	[D(10,5)]0 +[D(15)]1
(11,14)	5	[D(11,14)]0 +[D(12,13)]1
(11,2,12)	11	[D(11,2,12)]0 +[D(12,13)]1
(11,22)	13	[D(11,22)]0 +[D(13,2)]1
(11,3,1)	5	[D(11,3,1)]0 +[D(12,2,1)]1
(11,3,1)	11	[D(11,3,1)]0 +[D(13,12)]1
(11,3,1)	13	[D(11,3,1)]0 +[D(12,3)]1
(11,4)	5	[D(11,4)]0 +[D(13,2)]1
(11,4)	11	[D(11,4)]0 +[D(14,1)]1
(12,13)	5	[D(12,13)]0 +[D(13,12)]1
(12,3)	11	[D(12,3)]0 +[D(13,2)]1
(12,3)	13	[D(12,3)]0 +[D(15)]1
(13,12)	5	[D(13,12)]0 +[D(14,1)]1
(13,2)	13	[D(13,2)]0 +[D(14,1)]1
(14,1)	5	[D(14,1)]0 +[D(15)]1

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