{
  "id": "math/0403250",
  "version": "v2",
  "published": "2004-03-15T22:42:57.000Z",
  "updated": "2004-06-09T18:40:08.000Z",
  "title": "Finite dimensional representations of symplectic reflection algebras associated to wreath products",
  "authors": [
    "Pavel Etingof",
    "Silvia Montarani"
  ],
  "comment": "10 pages, latex",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "In this paper we construct finite dimensional representations of the wreath product symplectic reflection algebra H(k,c,N,G) of rank N attached to a finite subgroup G of SL(2,C) (here k is a number and c a class function on the set of nontrivial elements of G). Specifically, we show that if W is an irreducible representation of S_N whose Young diagram is a rectangle, and Y an irreduible finite dimensional representation of H(c,1,G), then the representation M=W\\otimes Y^N of H(0,c_0,N,G) can be deformed along a hyperplane in the space of parameters (k,c) passing through c_0. On the other hand, if Y is 1-dimensional and the Young diagram of W is not a rectangle, such a deformation does not exist.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-06-09T18:40:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "symplectic reflection algebras",
      "wreath product symplectic reflection algebra",
      "construct finite dimensional representations",
      "young diagram"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......3250E"
    }
  }
}