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arXiv · 0905.0407

Koszul duality of translation--and Zuckerman functors

Steen Ryom-Hansen
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Abstract

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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BibTeXRIS

Steen Ryom-Hansen. 2009-05-04. Koszul duality of translation--and Zuckerman functors. https://arxiv.org/abs/0905.0407

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