  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.
