A remark on rational Cherednik algebras and differential operators on the cyclic quiver

Gordon, I. (2006) A remark on rational Cherednik algebras and differential operators on the cyclic quiver. Glasgow Mathematical Journal, 48(1), pp. 145-160. (doi: 10.1017/S0017089505002946)

Abstract

We show that the spherical subalgebra Uk,c of the rational Cherednik algebra associated to Sn 2 Cl, the wreath product of the symmetric group and the cyclic group of order l, is isomorphic to a quotient of the ring of invariant differential operators on a space of representations of the cyclic quiver of size l. This confirms a version of [5, Conjecture 11.22] in the case of cyclic groups. The proof is a straightforward application of work of Oblomkov [12] on the deformed Harish–Chandra homomorphism, and of Crawley–Boevey, [3] and [4], and Gan and Ginzburg [7] on preprojective algebras.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: UNSPECIFIED
• Authors: Gordon, I.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Glasgow Mathematical Journal
• Publisher: Cambridge University Press
• ISSN: 0017-0895
• ISSN (Online): 1469-509X
• Published Online: 24 March 2006
• Copyright Holders: Copyright © 2006 Glasgow Mathematical Journal Trust
• First Published: First published in Glasgow Mathematical Journal 48(1):145-160
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher