Exponents for B-stable ideals
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Let be a simple algebraic group over the complex numbers containing a Borel subgroup . Given a -stable ideal in the nilradical of the Lie algebra of , we define natural numbers which we call ideal exponents. We then propose two conjectures where these exponents arise, proving these conjectures in types and some other types.
When , we recover the usual exponents of by Kostant (1959), and one of our conjectures reduces to a well-known factorization of the Poincaré 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.
E Sommers and J Tymoczko. "Exponents for B-stable ideals" Transaction of the American Mathematical Society 358.8 (2006): 3493-3509.
Available at: http://works.bepress.com/eric_sommers/3