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ON THE SMOOTHNESS OF CENTRES OF RATIONAL CHEREDNIK ALGEBRAS IN POSITIVE CHARACTERISTIC

Published online by Cambridge University Press:  01 October 2013

GWYN BELLAMY  and
MAURIZIO MARTINO
GWYN BELLAMY
Affiliation:
School of Mathematics and Statistics, University of Glasgow, 15 University Gardens, Glasgow G12 8QW, United Kingdom e-mail: gwyn.bellamy@glasgow.ac.uk
MAURIZIO MARTINO
Affiliation:
Mathematisches Institut, Endenicher Allee 60, 53115 Bonn, Germany e-mail: mmartino@math.uni-bonn.de
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Abstract

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In this paper we study rational Cherednik algebras at t = 1 in positive characteristic. We study a finite-dimensional quotient of the rational Cherednik algebra called the restricted rational Cherednik algebra. When the corresponding pseudo-reflection group belongs to the infinite series G(m, d, n), we describe explicitly the block decomposition of the restricted algebra. We also classify all pseudo-reflection groups for which the centre of the corresponding rational Cherednik algebra is regular for generic values of the deformation parameter.

Keywords

16G9916W70

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