Finite dimensional representations of W-algebras

Abstract

W-algebras of finite type are certain finitely generated associative algebras closely related to the 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 study a relation between Harish-Chandra bimodules and bimodules over $W$-algebras.

19 pages, v2, 21 pages, moderate changes, some mistakes fixed, Corollary 1.3.3 is added, v3 24 pages three new subsections and several remarks added v4 proof of Lemma 2.4.1 expanded, Remark 2.3.2 added, v5 29 pages major changes, v6 more changes, v7 final

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