{
  "id": "1612.05090",
  "version": "v1",
  "published": "2016-12-15T14:50:50.000Z",
  "updated": "2016-12-15T14:50:50.000Z",
  "title": "Towards a Classification of Finite-Dimensional Representations of Rational Cherednik Algebras of Type D",
  "authors": [
    "Seth Shelley-Abrahamson",
    "Alec Sun"
  ],
  "comment": "12 pages",
  "categories": [
    "math.RT",
    "math.CO"
  ],
  "abstract": "Using a combinatorial description due to Jacon and Lecouvey of the wall crossing bijections for cyclotomic rational Cherednik algebras, we show that the irreducible representations $L_c(\\lambda^\\pm)$ of the rational Cherednik algebra $H_c(D_n, \\mathbb{C}^n)$ of type $D$ for symmetric bipartitions $\\lambda$ are infinite dimensional for all parameters $c$. In particular, all finite-dimensional irreducible representations of rational Cherednik algebras of type $D$ arise as restrictions of finite-dimensional irreducible representations of rational Cherednik algebras of type $B$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-15T14:50:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite-dimensional representations",
      "finite-dimensional irreducible representations",
      "classification",
      "cyclotomic rational cherednik algebras",
      "combinatorial description"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}