Whittaker coinvariants for GL(m|n)

Abstract

Abstract Let W m | n be the (finite) W-algebra attached to the principal nilpotent orbit in the general linear Lie superalgebra gl m | n ( C ) . In this paper we study the Whittaker coinvariants functor, which is an exact functor from category O for gl m | n ( C ) to a certain category of finite-dimensional modules over W m | 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 W m | n explicitly, and deduce consequences for the classification of blocks of O up to Morita/derived equivalence.