{
  "id": "2102.09064",
  "version": "v1",
  "published": "2021-02-17T23:00:55.000Z",
  "updated": "2021-02-17T23:00:55.000Z",
  "title": "Simple weight modules with finite weight multiplicities over the Lie algebra of polynomial vector fields",
  "authors": [
    "Dimitar Grantcharov",
    "Vera Serganova"
  ],
  "comment": "22 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let ${\\mathcal W}_n$ be the Lie algebra of polynomial vector fields. We classify simple weight ${\\mathcal W}_n$-modules $M$ with finite weight multiplicities. We prove that every such nontrivial module $M$ is either a tensor module or the unique simple submodule in a tensor module associated with the de Rham complex on $\\mathbb C^n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-17T23:00:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B66",
      "17B10"
    ],
    "keywords": [
      "polynomial vector fields",
      "finite weight multiplicities",
      "simple weight modules",
      "lie algebra",
      "tensor module"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}