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

Gwyn Bellamy; Maurizio Martino

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arxiv 1112.3835 v1 pith:4W5UY53M submitted 2011-12-16 math.RA math.RT

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

Gwyn Bellamy , Maurizio Martino This is my paper

classification math.RA math.RT

keywords cherednikrationalalgebraalgebrascharacteristiccorrespondingpositivepseudo-reflection

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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.

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

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