{
  "id": "2307.06603",
  "version": "v1",
  "published": "2023-07-13T07:56:19.000Z",
  "updated": "2023-07-13T07:56:19.000Z",
  "title": "Representations of the rational Cherednik algebra $H_{t,c}(S_3,\\h)$ in positive characteristic",
  "authors": [
    "Martina Balagovic",
    "Jordan Barnes"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "We study the rational Cherednik algebra $H_{t,c}(S_3,\\h)$ of type $A_2$ in positive characteristic $p$, and its irreducible category $\\mathcal{O}$ representations $L_{t,c}(\\tau)$. For every possible value of $p,t,c$, and $\\tau$ we calculate the Hilbert polynomial and the character of $L_{t,c}(\\tau)$, and give explicit generators of the maximal proper graded submodule of the Verma module.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-13T07:56:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "rational cherednik algebra",
      "positive characteristic",
      "representations",
      "maximal proper graded submodule",
      "hilbert polynomial"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}