On the smoothness of centres of rational Cherednik algebras in positive characteristic

Details On the smoothness of centres of rational Cherednik algebras in positive characteristic On the smoothness of centres of rational Cherednik algebras in positive characteristic

2011-12-16

arxiv.org/abs/1112.3835v1

Mathematics

Rings and Algebras

Scientific paper

In this article 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.

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