Exponents for B-stable ideals

被引:34
作者
Sommers, E [1 ]
Tymoczko, J
机构
[1] Univ Massachusetts, Dept Math & Stat, Amherst, MA 01003 USA
[2] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA
关键词
D O I
10.1090/S0002-9947-06-04080-3
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Let G be a simple algebraic group over the complex numbers containing a Borel subgroup B. Given a B-stable ideal I in the nilradical of the Lie algebra of B, we de. ne natural numbers m(1), m(2),..., m(k) which we call ideal exponents. We then propose two conjectures where these exponents arise, proving these conjectures in types A(n), B-n, C-n and some other types. When I = 0, we recover the usual exponents of G by Kostant ( 1959), and one of our conjectures reduces to a well-known factorization of the Poincare polynomial of the Weyl group. The other conjecture reduces to a well-known result of Arnold-Brieskorn on the factorization of the characteristic polynomial of the corresponding Coxeter hyperplane arrangement.
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页码:3493 / 3509
页数:17
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