Hyperplane arrangements associated to symplectic quotient singularities

Bellamy, G. , Schedler, T. and Thiel, U. (2018) Hyperplane arrangements associated to symplectic quotient singularities. Banach Centre Publications, 116, pp. 25-45. (doi: 10.4064/bc116-2)

Abstract

We study the hyperplane arrangements associated, via the minimal model programme, to symplectic quotient singularities. We show that this hyperplane arrangement equals the arrangement of CM-hyperplanes coming from the representation theory of restricted rational Cherednik algebras. We explain some of the interesting consequences of this identification for the representation theory of restricted rational Cherednik algebras. We also show that the Calogero–Moser space is smooth if and only if the Calogero–Moser families are trivial. We describe the arrangements of CM-hyperplanes associated to several exceptional complex reflection groups, some of which are free.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Bellamy, Professor Gwyn
• Authors: Bellamy, G., Schedler, T., and Thiel, U.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Banach Centre Publications
• Publisher: Institute of Mathematics, Polish Academy of Sciences
• ISSN: 0137-6934
• ISSN (Online): 1730-6299
• Copyright Holders: Copyright © 2018 Polish Academy of Sciences
• First Published: First published in Banach Centre Publications 116:25-45
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher