On deformation quantizations of hypertoric varieties

Gwyn Bellamy and Toshiro Kuwabara

Vol. 260 (2012), No. 1, 89–127

DOI: 10.2140/pjm.2012.260.89

Abstract

Based on a construction by Kashiwara and Rouquier, we present an analogue of the Beilinson–Bernstein localization theorem for hypertoric varieties. In this case, sheaves of differential operators are replaced by sheaves of W-algebras. As a special case, our result gives a localization theorem for rational Cherednik algebras associated to cyclic groups.

Keywords

deformation quantization, hypertoric varieties

Mathematical Subject Classification 2010

Primary: 14A22, 16S80

Secondary: 18E35

Milestones

Received: 22 July 2011

Accepted: 25 May 2012

Published: 11 October 2012