{
  "id": "math/0501156",
  "version": "v1",
  "published": "2005-01-11T11:36:22.000Z",
  "updated": "2005-01-11T11:36:22.000Z",
  "title": "Finite dimensional representations of symplectic reflection algebras associated to wreath products II",
  "authors": [
    "Silvia Montarani"
  ],
  "comment": "10 pages, Latex",
  "categories": [
    "math.RT"
  ],
  "abstract": "This note extends some results of a previous paper (math.RT/0403250) about 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, let N'=(N_1,...,N_r) be a partition of N. Consider W=W_1\\otimes >...\\otimes W_r an irreducible representation of S_N'=S_{N_1}\\times ...\\times S_{N_r}\\subset S_N s.t. W_i has rectangular Young diagram for any i and let {Y_i}, i=1,...,r be a collection of irreducible non isomorphic representation of the rank 1 algebra B=H(c_0,1,G) s.t. Ext^1_B(Y_i, Y_j)=0 for any i\\neq j. Consider the module M'=W\\otimes Y, where Y=Y_1^{N_1}\\otimes ...\\otimes Y_r^{N_r}, over the subalgebra S_N'#B^N \\subset S_N#B^N= H(0,c_0,N,G) and form the induced module M over H(0,c_0,N,G). We show that M can be uniquely deformed along a linear subspace of codimension r in the space of the parameters (k,c) passing through c_0. This result implies the main result of math.RT/0403250 as a particular case, the case of the trivial partition N'=(N).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-01-11T11:36:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite dimensional representations",
      "symplectic reflection algebras",
      "wreath product symplectic reflection algebra",
      "non isomorphic representation"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......1156M"
    }
  }
}