B-stable ideals in the nilradical of a Borel subalgebra

被引：47

作者：

Sommers, EN ^{[1
]}

机构：

[1] Univ Massachusetts, Amherst, MA 01003 USA

[2] Inst Adv Study, Princeton, NJ 08540 USA

来源：

CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES | 2005年 / 48卷 / 03期

关键词：

D O I：

10.4153/CMB-2005-043-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We count the number of strictly positive B-stable ideals in the nilradical of a Borel subalgebra and prove that the minimal roots of any B-stable ideal are conjugate by an element of the Weyl group to a subset of the simple roots. We also count the number of ideals whose minimal roots are conjugate to a fixed subset of simple roots.

引用

页码：460 / 472

页数：13

共 16 条

[1] Generalized catalan numbers, Weyl groups and arrangements of hyperplanes
Athanasiadis, CA
[J]. BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2004, 36 : 294 - 302
[2] Broer A, 1998, NATO ADV SCI I C-MAT, V514, P39
[3] ad-nilpotent ideals of a Borel subalgebra
Cellini, P
Papi, P
[J]. JOURNAL OF ALGEBRA, 2000, 225 (01) : 130 - 141
[4] Ad-nilpotent ideals of a Borel subalgebra II
Cellini, P
Papi, P
[J]. JOURNAL OF ALGEBRA, 2002, 258 (01) : 112 - 121
[5] Douglass J.M., 1999, REPRESENT THEOR, V3, P444
[6] FAN CK, 1996, TRANSFORM GROUPS, V1, P35, DOI DOI 10.1007/BF02587734.MR1390748
[7] Y-systems and generalized associahedra
Fomin, S
Zelevinsky, A
[J]. ANNALS OF MATHEMATICS, 2003, 158 (03) : 977 - 1018
[8] CONJECTURES ON THE QUOTIENT RING BY DIAGONAL INVARIANTS
HAIMAN, MD
[J]. JOURNAL OF ALGEBRAIC COMBINATORICS, 1994, 3 (01) : 17 - 76
[9] On a family of hyperplane arrangements related to the affine Weyl groups
Headley, P
[J]. JOURNAL OF ALGEBRAIC COMBINATORICS, 1997, 6 (04) : 331 - 338
[10] ORLIK P, 1983, P SYMP PURE MATH, V40, P269

← 1 2 →