{
  "id": "math/0507413",
  "version": "v1",
  "published": "2005-07-20T21:29:27.000Z",
  "updated": "2005-07-20T21:29:27.000Z",
  "title": "A remark on rational Cherednik algebras and differential operators on the cyclic quiver",
  "authors": [
    "Iain Gordon"
  ],
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "We show that the spherical subalgebra of the rational Cherednik algebra associated to the wreath product of a symmetric group and a cyclic group is isomorphic to a quotient of the ring of invariant differential operators on a space of representations of the cyclic quiver. This confirms a version of a conjecture of Etingof and Ginzburg in the case of cyclic groups. The proof is a straightforward application of work of Oblomkov on the deformed Harish-Chandra homomorphism, and of Crawley-Boevey and of Gan and Ginzburg on preprojective algebras.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-07-20T21:29:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cyclic quiver",
      "cyclic group",
      "invariant differential operators",
      "symmetric group",
      "wreath product"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......7413G"
    }
  }
}