Whittaker coinvariants for GL(m|n)

Abstract

Let Wm|n be the (finite) W-algebra attached to the principal nilpotent orbit in the general linear Lie superalgebra glm|n(C). In this paper we study the Whittaker coinvariants functor, which is an exact functor from category O for glm|n(C) to a certain category of finite-dimensional modules over Wm|n. We show that this functor has properties similar to Soergel's functor V in the setting of category O for a semisimple Lie algebra. We also use it to compute the center of Wm|n explicitly, and deduce consequences for the classification of blocks of O up to Morita/derived equivalence.