{
  "id": "1106.5094",
  "version": "v2",
  "published": "2011-06-25T02:27:35.000Z",
  "updated": "2017-11-28T17:59:17.000Z",
  "title": "Unitary representations of cyclotomic rational Cherednik algebras",
  "authors": [
    "Stephen Griffeth"
  ],
  "comment": "39 pages; version 2 contains major changes: a new title to more accurately reflect content, greatly expanded exposition, completely explicit results for r=2. Also: pictures!",
  "categories": [
    "math.RT",
    "math.CO"
  ],
  "abstract": "We classify the irreducible unitary modules in category O for the rational Cherednik algebras of type G(r,1,n) and give explicit combinatorial formulas for their graded characters. More precisely, we produce a combinatorial algorithm determining, for each r-partition of n, the closed semi-linear set of parameters for which the contravariant form on the irreducible representation with the given r-partition as lowest weight is positive definite. We use this algorithm to give a closed form answer for the Cherednik algebra of the symmetric group (recovering a result of Etingof-Stoica and the author) and the Weyl groups of classical type.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-06-25T02:27:35.000Z",
      "title": "Unitary representations of rational Cherednik algebras, II",
      "abstract": "The goal of this paper is to classify the unitary irreducible modules in category O for the rational Cherednik algebras of type G(r,1,n). As a first step, we classify those irreducibles in O that are diagonalizable with respect to a commutative subalgebra introduced by Dunkl and Opdam. As a byproduct, we obtain combinatorial character formulas for many irreducible modules in category O, in terms of certain column-strict tableaux.",
      "comment": "20 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2017-11-28T17:59:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E05",
      "05E10",
      "05E15",
      "16S35",
      "20C30",
      "16D90",
      "16S38",
      "16T30"
    ],
    "keywords": [
      "rational cherednik algebras",
      "unitary representations",
      "combinatorial character formulas",
      "unitary irreducible modules",
      "first step"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 39,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1106.5094G"
    }
  }
}