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

2011/12/16 by Gwyn Bellamy, Bellamy, Gwyn, Maurizio Martino +1
Mathematics · #13D05 #16G99 #16R99 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #Rings and Algebras (math.RA) #math.RA #math.RT #msc:13D05 #msc:16G99 #msc:16R99

paper · pdf · doi:10.48550/arxiv.1112.3835

arxiv created 2011/12/16 · openalex publication_date 2011/12/16 · arxiv updated 2011/12/19 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

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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