{
  "id": "2311.06619",
  "version": "v1",
  "published": "2023-11-11T17:29:31.000Z",
  "updated": "2023-11-11T17:29:31.000Z",
  "title": "Irreducible representations of $\\textrm{GL}_n(\\mathbb{C})$ of minimal Gelfand-Kirillov dimension",
  "authors": [
    "Zhanqiang Bai",
    "Yangyang Chen",
    "Dongwen Liu",
    "Binyong Sun"
  ],
  "comment": "To appear in Acta Mathematica Sinica, English Series",
  "categories": [
    "math.RT"
  ],
  "abstract": "In this article, by studying the Bernstein degrees and Goldie rank polynomials, we establish a comparison between the irreducible representations of $G=\\textrm{GL}_n(\\mathbb{C})$ possessing the minimal Gelfand-Kirillov dimension and those induced from finite-dimensional representations of the maximal parabolic subgroup of $G$ of type $(n-1,1)$. We give the transition matrix between the two bases for the corresponding coherent families.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-11T17:29:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E46",
      "22E47"
    ],
    "keywords": [
      "minimal gelfand-kirillov dimension",
      "irreducible representations",
      "goldie rank polynomials",
      "maximal parabolic subgroup",
      "finite-dimensional representations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}