{
  "id": "2212.12625",
  "version": "v1",
  "published": "2022-12-24T01:03:17.000Z",
  "updated": "2022-12-24T01:03:17.000Z",
  "title": "The Koszul complex and a certain induced module for a quantum group",
  "authors": [
    "Toshiyuki Tanisaki"
  ],
  "comment": "35 pages",
  "categories": [
    "math.RT",
    "math.QA"
  ],
  "abstract": "We give a description of a certain induced module for a quantum group of type $A$. Together with our previous results this gives a proof of Lusztig's conjectural multiplicity formula for non-restricted modules over the De Concini-Kac type quantized enveloping algebra of type $A_n$ at the $\\ell$-th root of unity, where $\\ell$ is an odd integer satisfying $\\ell\\geqq n+1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-24T01:03:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G42",
      "17B37"
    ],
    "keywords": [
      "quantum group",
      "induced module",
      "koszul complex",
      "lusztigs conjectural multiplicity formula",
      "concini-kac type quantized enveloping algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}