Semisimplicity of the category of admissible D-modules

Bellamy, G. and Boos, M. (2021) Semisimplicity of the category of admissible D-modules. Kyoto Journal of Mathematics, 61(1), pp. 115-170. (doi: 10.1215/21562261-2020-0006)

181271.pdf - Accepted Version



Using a representation theoretic parameterization for the orbits in the enhanced cyclic nilpotent cone as derived by the authors in a previous article, we compute the fundamental group of these orbits. This computation has several applications to the representation theory of the category of admissible D-modules on the space of representations of the framed cyclic quiver. First and foremost, we compute precisely when this category is semisimple. We also show that the category of admissible D-modules has enough projectives. Finally, the support of an admissible D-module is contained in a certain Lagrangian in the cotangent bundle of the space of representations. Thus, taking these characteristic cycles defines a map from the K-group of the category of admissible D-modules to the Z-span of the irreducible components of this Lagrangian. We show that this map is always injective, and is a bijection if and only if the monodromicity parameter is integral.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Bellamy, Professor Gwyn
Authors: Bellamy, G., and Boos, M.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Kyoto Journal of Mathematics
Publisher:Duke University Press
ISSN (Online):2154-3321
Published Online:14 December 2020
Copyright Holders:Copyright © 2021 Kyoto University
First Published:First published in Kyoto Journal of Mathematics 61(1): 115-170
Publisher Policy:Reproduced in accordance with the publisher copyright policy
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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
662571Symplectic representation theoryGwyn BellamyEngineering and Physical Sciences Research Council (EPSRC)EP/N005058/1M&S - MATHEMATICS