Hamiltonian reduction and nearby cycles for mirabolic D-modules

Bellamy, G. and Ginzburg, V. (2015) Hamiltonian reduction and nearby cycles for mirabolic D-modules. Advances in Mathematics, 269, pp. 71-161. (doi:10.1016/j.aim.2014.10.002)

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Publisher's URL: http://dx.doi.org/10.1016/j.aim.2014.10.002

Abstract

We study holonomic D-modules on SL_n(C)xC^n, called mirabolic modules, analogous to Lusztig's character sheaves. We describe the supports of simple mirabolic modules. We show that a mirabolic module is killed by the functor of Hamiltonian reduction from the category of mirabolic modules to the category of representations of the trigonometric Cherednik algebra if and only if the characteristic variety of the module is contained in the unstable locus. We introduce an analogue of the Verdier specialization functor for representations of Cherednik algebras which agrees, on category O, with the restriction functor of Bezrukavnikov and Etingof. In type A, we also consider a Verdier specialization functor on mirabolic D-modules. We show that Hamiltonian reduction intertwines specialization functors on mirabolic D-modules with the corresponding functors on representations of the Cherednik algebra. This allows us to apply known purity results for nearby cycles in the setting considered by Bezrukavnikov and Etingof.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Bellamy, Dr Gwyn
Authors: Bellamy, G., and Ginzburg, V.
Subjects:Q Science > QA Mathematics
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Advances in Mathematics
Publisher:Elsevier Inc.
ISSN:0001-8708
ISSN (Online):1090-2082
Copyright Holders:Copyright © 2014 Elsevier Inc.
First Published:First published in Advances in Mathematics 269:71-161
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher
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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
620601Geometric methods in representation theory of rational Cherednik algebrasGwyn BellamyEngineering & Physical Sciences Research Council (EPSRC)EP/H028153/1M&S - MATHEMATICS