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Differential operators on quantized flag manifolds at roots of unity, II

Published online by Cambridge University Press:  11 January 2016

Toshiyuki Tanisaki
Toshiyuki Tanisaki*
Affiliation:
Department of Mathematics Osaka City University Sumiyoshi-ku, Osaka 558-8585Japantanisaki@sci.osaka-cu.ac.jp
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Abstract

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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.

Keywords

20G0517B37
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 214 , June 2014 , pp. 1 - 52
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2014

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