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Journal of Lie Theory 14 (2004), No. 1, 151--163
Copyright Heldermann Verlag 2004

Koszul Duality of Translation -- and Zuckerman Functors

Steen Ryom-Hansen
Matematisk Afdeling, Universitetsparken 5, 2100 København Ø, Danmark, steen@math.ku.dk

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.

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