{
  "id": "0806.2605",
  "version": "v1",
  "published": "2008-06-16T15:16:40.000Z",
  "updated": "2008-06-16T15:16:40.000Z",
  "title": "Simplicity of vacuum modules over affine Lie superalgebras",
  "authors": [
    "Crystal Hoyt",
    "Shifra Reif"
  ],
  "comment": "16 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "We prove an explicit condition on the level $k$ for the irreducibility of a vacuum module $V^{k}$ over a (non-twisted) affine Lie superalgebra, which was conjectured by M. Gorelik and V.G. Kac. An immediate consequence of this work is the simplicity conditions for the corresponding minimal W-algebras obtained via quantum reduction, in all cases except when the level $k$ is a non-negative integer.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-06-16T15:16:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "affine lie superalgebra",
      "vacuum module",
      "explicit condition",
      "immediate consequence",
      "simplicity conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0806.2605H"
    }
  }
}