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- W2952626241 abstract "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." @default.
- W2952626241 created "2019-06-27" @default.
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- W2952626241 date "2004-06-02" @default.
- W2952626241 modified "2023-09-27" @default.
- W2952626241 title "Exponents for B-stable ideals" @default.
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