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June 2014 Differential operators on quantized flag manifolds at roots of unity, II
Toshiyuki Tanisaki
Nagoya Math. J. 214: 1-52 (June 2014). DOI: 10.1215/00277630-2402198

Abstract

We formulate a Beilinson–Bernstein-type derived equivalence for a quantized enveloping algebra at a root of 1 as a conjecture. It says that there exists a derived equivalence between the category of modules over a quantized enveloping algebra at a root of 1 with fixed regular Harish-Chandra central character and the category of certain twisted D-modules on the corresponding quantized flag manifold. We show that the proof is reduced to a statement about the (derived) global sections of the ring of differential operators on the quantized flag manifold. We also give a reformulation of the conjecture in terms of the (derived) induction functor.

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Toshiyuki Tanisaki. "Differential operators on quantized flag manifolds at roots of unity, II." Nagoya Math. J. 214 1 - 52, June 2014. https://doi.org/10.1215/00277630-2402198

Information

Published: June 2014
First available in Project Euclid: 7 January 2014

zbMATH: 1311.14047
MathSciNet: MR3211817
Digital Object Identifier: 10.1215/00277630-2402198

Subjects:
Primary: 20G05
Secondary: 17B37

Rights: Copyright © 2014 Editorial Board, Nagoya Mathematical Journal

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Vol.214 • June 2014
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