Koszul Duality of Translation -- and Zuckerman Functors

摘要

We review Koszul duality in the representation theory of the category O; in particular, we give a new presentation of the Koszul duality functor. Combining this with work of Backelin, we show that the translation and Zuckerman functors are Koszul dual to each other, thus verifying a conjecture of Bernstein, Frenkel and Khovanov. Finally we use Koszul duality to give a short proof of the Enright-Shelton equivalence.