{
  "id": "1811.00332",
  "version": "v1",
  "published": "2018-11-01T11:58:42.000Z",
  "updated": "2018-11-01T11:58:42.000Z",
  "title": "Harish-Chandra modules over invariant subalgebras in a skew-group ring",
  "authors": [
    "Volodymyr Mazorchuk",
    "Elizaveta Vishnyakova"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "We construct a new class of algebras resembling enveloping algebras and generalizing orthogonal Gelfand-Zeitlin algebras and rational Galois algebras studied by [EMV,FGRZ,RZ,Har]. The algebras are defined via a geometric realization in terms of sheaves of functions invariant under an action of a finite group. A natural class of modules over these algebra can be constructed via a similar geometric realization. In the special case of a local reflection group, these modules are shown to have an explicit basis, generalizing similar results for orthogonal Gelfand-Zeitlin algebras from [EMV] and for rational Galois algebras from [FGRZ]. We also give a sufficient conditions for simplicity of these modules.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-01T11:58:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "harish-chandra modules",
      "invariant subalgebras",
      "rational galois algebras",
      "skew-group ring",
      "local reflection group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}