Exponents for B-stable ideals

dc.creatorSommers, Eric
dc.creatorTymoczko, Julianna
dc.date2004-06-02
dc.date.accessioned2026-07-07T05:08:49Z
dc.date.available2026-07-07T05:08:49Z
dc.descriptionLet 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.description17 pages
dc.identifierhttps://arxiv.org/abs/math/0406047
dc.identifierhttp://arxiv.org/abs/math/0406047
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/71415
dc.subjectRepresentation Theory
dc.subjectCombinatorics
dc.subject20G05
dc.titleExponents for B-stable ideals
dc.typetext

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