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)
|
Text
181271.pdf - Accepted Version 608kB |
Abstract
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 |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| 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: | 2156-2261 |
| 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 |
| Related URLs: |
University Staff: Request a correction | Enlighten Editors: Update this record
Funder and Project Information
Funder and Project Information