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Bezrukavnikov, Roman; Finkelberg, Michael; Ostrik, Victor

Character \(D\)-modules via Drinfeld center of Harish-Chandra bimodules. (English) Zbl 1267.20058

Invent. Math. 188, No. 3, 589-620 (2012).
The main result of this paper realizes the category of character \(D\)-modules as the Drinfeld center of the Abelian monoidal category of Harish-Chandra bimodules. As an application, the authors give a new proof for Lusztig’s classification of irreducible character sheaves over \(\mathbb C\) (under a mild technical assumption), a simple description for the top cohomology of convolution of character sheaves over \(\mathbb C\) in a given cell modulo smaller cells and relate the Harish-Chandra functor to Verdier specialization in the De Concini-Procesi compactification.
Reviewer: Volodymyr Mazorchuk (Uppsala)

Cited in 1 Review
Cited in 26 Documents

MSC:

20G05 Representation theory for linear algebraic groups
17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
18E10 Abelian categories, Grothendieck categories
46M05 Tensor products in functional analysis

Keywords:

Drinfeld center; Harish-Chandra bimodules; irreducible character sheaves; convolution of \(D\)-modules; cells; category \(\mathcal O\); Abelian monoidal categories
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References:

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