{
  "id": "2107.07323",
  "version": "v1",
  "published": "2021-07-15T13:48:32.000Z",
  "updated": "2021-07-15T13:48:32.000Z",
  "title": "$\\mathfrak{sl}_2$-Harish-Chandra modules for $\\mathfrak{sl}_2 \\ltimes L(4)$",
  "authors": [
    "Volodymyr Mazorchuk",
    "Rafael Mrđen"
  ],
  "categories": [
    "math.RT",
    "math.CO"
  ],
  "abstract": "We use analogues of Enright's and Arkhipov's functors to determine the quiver and relations for a category of $\\mathfrak{sl}_2 \\ltimes L(4)$-modules which are locally finite (and with finite multiplicities) over $\\mathfrak{sl}_2$. We also outline serious obstacles to extend our result to $\\mathfrak{sl}_2 \\ltimes L(k)$, for $k>4$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-07-15T13:48:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "harish-chandra modules",
      "arkhipovs functors",
      "finite multiplicities",
      "locally finite"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}