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Article Dans Une Revue Duke Mathematical Journal Année : 2010

Koszul duality and modular representations of semi-simple Lie algebras

Résumé

In this paper we prove that if G is a connected, simply-connected, semi-simple algebraic group over an algebraically closed field of sufficiently large characteristic, then all the blocks of the restricted enveloping algebra of the Lie algebra of G can be endowed with a Koszul grading (extending results of Andersen, Jantzen, Soergel). We also give information about the Koszul dual rings. In the case of the block associated to a regular character x of the Harish-Chandra center, the dual ring is related to modules over the enveloping algebra specialized at x, with generalized trivial Frobenius character. Our main tool is the localization theory developed by Bezrukavnikov, Mirkovic, Rumynin.
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Dates et versions

hal-00476255 , version 1 (25-04-2010)

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  • HAL Id : hal-00476255 , version 1

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Simon Riche. Koszul duality and modular representations of semi-simple Lie algebras. Duke Mathematical Journal, 2010, 154, pp.31-134. ⟨hal-00476255⟩
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