An explicit presentation of the centre of the restricted rational Cherednik algebra

Abstract

In this paper we give an explicit presentation of the centre of the restricted rational Cherednik algebra $\overline{H}_c(S_n\wr\mathbb{Z}/\ell\mathbb{Z})$ for a particular choice of parameter $c$. More precisely, we describe the centre of the indecomposable blocks of $\overline{H}_c(S_n\wr\mathbb{Z}/\ell\mathbb{Z})$ in terms of generators and relations. The parameters $c$ for which this presentation is valid are such that the Calogero-Moser space is smooth. Furthermore, we demonstrate how the explicit presentation of the centre of $\overline{H}_c(S_n\wr\mathbb{Z}/\ell\mathbb{Z})$ can be directly derived from the set of $\ell$-multipartitions of $n$.