{
  "id": "0912.1578",
  "version": "v1",
  "published": "2009-12-08T20:09:29.000Z",
  "updated": "2009-12-08T20:09:29.000Z",
  "title": "Catalan numbers for complex reflection groups",
  "authors": [
    "Iain Gordon",
    "Stephen Griffeth"
  ],
  "comment": "9 pages",
  "categories": [
    "math.CO",
    "math.RT"
  ],
  "abstract": "We construct (q,t)-Catalan polynomials and q-Fuss-Catalan polynomials for any irreducible complex reflection group W. The two main ingredients in this construction are Rouquier's formulation of shift functors for the rational Cherednik algebras of W, and Opdam's analysis of permutations of the irreducible representations of W arising from the Knizhnik-Zamolodchikov connection.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-12-08T20:09:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E10",
      "16G99"
    ],
    "keywords": [
      "catalan numbers",
      "irreducible complex reflection group",
      "rational cherednik algebras",
      "q-fuss-catalan polynomials",
      "main ingredients"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0912.1578G"
    }
  }
}