Journal of Lie Theory EMIS ELibM Electronic Journals Journal of Lie Theory
Vol. 14, No. 1, pp. 151--163 (2004)

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Koszul duality of translation---and Zuckerman functors

Steen Ryom-Hansen

Steen Ryom-Hansen
Matematisk Afdeling
Universitetsparken 5
DK-2100 K{ø}benhavn Ø
Danmark
steen@math.ku.dk

Abstract: We review Koszul duality in the representation theory of the category $\cal O$; 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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Electronic version published on: 29 Jan 2004. This page was last modified: 1 Sep 2004.

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