{
  "id": "2301.03316",
  "version": "v1",
  "published": "2023-01-09T13:11:55.000Z",
  "updated": "2023-01-09T13:11:55.000Z",
  "title": "An explicit presentation of the centre of the restricted rational Cherednik algebra",
  "authors": [
    "Niall Hird"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "In this paper we give an explicit presentation of the centre of the restricted rational Cherednik algebra $\\overline{H}_c(S_n\\wr\\mathbb{Z}/\\ell\\mathbb{Z})$. 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 $n$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-01-09T13:11:55.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "restricted rational cherednik algebra",
      "explicit presentation",
      "calogero-moser space",
      "result holds",
      "multipartitions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}