FINITE DIMENSIONAL REPRESENTATIONS OF W-ALGEBRAS

Abstract

W-algebras of finite type are certain finitely generated associative algebras closely related to universal enveloping algebras of semisimple Lie algebras. In this paper we prove a conjecture of Premet that gives an almost complete classification of finite dimensional irreducible modules for W-algebras. Also we get some partial results towards a conjecture by Ginzburg on their finite dimensional bimodules.