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

In this paper we give an explicit presentation of the centre of the restricted rational Cherednik algebra ${\bar{H}}_c(S_n\wr \mathbb{Z}\mathrm{/}\mathrm{\ell }\mathbb{Z})$ for a particular choice of parameter $c$. More precisely, we describe the centre of the indecomposable blocks of ${\bar{H}}_c(S_n\wr \mathbb{Z}\mathrm{/}\mathrm{\ell }\mathbb{Z})$ 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 ${\bar{H}}_c(S_n\wr \mathbb{Z}\mathrm{/}\mathrm{\ell }\mathbb{Z})$ can be directly derived from the set of $\mathrm{\ell }$-multipartitions of $n$.