Exponents for B-stable ideals
| dc.creator | Sommers, Eric | |
| dc.creator | Tymoczko, Julianna | |
| dc.date | 2004-06-02 | |
| dc.date.accessioned | 2026-07-07T05:08:49Z | |
| dc.date.available | 2026-07-07T05:08:49Z | |
| dc.description | 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 define 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 is zero, we recover the usual exponents of G by Kostant 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. | |
| dc.description | 17 pages | |
| dc.identifier | https://arxiv.org/abs/math/0406047 | |
| dc.identifier | http://arxiv.org/abs/math/0406047 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71415 | |
| dc.subject | Representation Theory | |
| dc.subject | Combinatorics | |
| dc.subject | 20G05 | |
| dc.title | Exponents for B-stable ideals | |
| dc.type | text |