Projective and Whittaker functors on category O

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. (C) 2021 Elsevier Inc. All rights reserved.

Automated summary

The Whittaker functor in 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 the equivalence between the category of Whittaker modules and a singular block of O proposed by Soergel and Milicic. It is shown that the Whittaker functor is a quotient functor that commutes with all projective functors and endomorphisms between them.