Koszul duality of translation--and Zuckerman functors

Details Koszul duality of translation--and Zuckerman functors Koszul duality of translation--and Zuckerman functors

2009-05-04

arxiv.org/abs/0905.0407v1

Mathematics

Representation Theory

Published version, Journal of Lie Theory

Scientific paper

We review Koszul duality in representation theory of category $ \cal 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.

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