Projective and Whittaker functors on category O

Abstract

Abstract We show that the Whittaker functor on a regular block of the BGG-category O of a semisimple complex Lie algebra can be obtained by composing a translation to the wall functor with Soergel and Milicic s equivalence between the category of Whittaker modules and a singular block of O . We show that the Whittaker functor is a quotient functor that commutes with all projective functors and endomorphisms between them.