{
  "id": "math/0212036",
  "version": "v4",
  "published": "2002-12-03T20:59:59.000Z",
  "updated": "2003-06-26T02:56:31.000Z",
  "title": "On the category O for rational Cherednik algebras",
  "authors": [
    "Victor Ginzburg",
    "Nicolas Guay",
    "Eric Opdam",
    "Raphael Rouquier"
  ],
  "comment": "28 pp., LaTeX, final version, to appear in Invent. Math",
  "categories": [
    "math.RT",
    "math.AG",
    "math.QA",
    "math.RA"
  ],
  "abstract": "We study the category O of representations of the rational Cherednik algebra A attached to a complex reflection group W. We construct an exact functor, called Knizhnik-Zamolodchikov functor, from O to the category of H-modules, where H is the (finite) Iwahori-Hecke algebra associated to W. We prove that the Knizhnik-Zamolodchikov functor induces an equivalence between O/O_tor, the quotient of O by the subcategory of A-modules supported on the discriminant and the category of finite-dimensional H-modules. The standard A-modules go, under this equivalence, to certain modules arising in Kazhdan-Lusztig theory of ``cells'', provided W is a Weyl group and the Hecke algebra H has equal parameters. We prove that the category O is equivalent to the module category over a finite dimensional algebra, a generalized \"q-Schur algebra\" associated to W.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2003-06-26T02:56:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "rational cherednik algebra",
      "finite dimensional algebra",
      "complex reflection group",
      "knizhnik-zamolodchikov functor induces",
      "module category"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}