{
  "id": "1304.5458",
  "version": "v1",
  "published": "2013-04-19T16:02:07.000Z",
  "updated": "2013-04-19T16:02:07.000Z",
  "title": "Classification of simple $W_n$-modules with finite-dimensional weight spaces",
  "authors": [
    "Yuly Billig",
    "Vyacheslav Futorny"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "We classify all simple $W_n$-modules with finite-dimensional weight spaces. Every such module is either of a highest weight type or is a quotient of a module of tensor fields on a torus, which was conjectured by Eswara Rao. This generalizes the classical result of Mathieu on simple weight modules for the Virasoro algebra. In our proof of the classification we construct a functor from the category of cuspidal $W_n$-modules to the category of $W_n$-modules with a compatible action of the algebra of functions on a torus. We also present a new identity for certain quadratic elements in the universal enveloping algebra of $W_1$, which provides important information about cuspidal $W_1$-modules.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-04-19T16:02:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10",
      "17B66"
    ],
    "keywords": [
      "finite-dimensional weight spaces",
      "classification",
      "highest weight type",
      "simple weight modules",
      "eswara rao"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1304.5458B"
    }
  }
}