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

Niall Hird

Published 2023-01-09Version 1

In this paper we give an explicit presentation of the centre of the restricted rational Cherednik algebra $\overline{H}_c(S_n\wr\mathbb{Z}/\ell\mathbb{Z})$. 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. This presentation is valid for any $c$ such that the Calogero-Moser space is smooth. In particular, the result holds for generic $c$. 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 $n$