Koszul duality of translation--and Zuckerman functors

Abstract

We review Koszul duality in representation theory of category $\mathcal{O}$, especially 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.

arXiv commentPublished version, Journal of Lie Theory

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