{
  "id": "2005.11536",
  "version": "v1",
  "published": "2020-05-23T13:38:43.000Z",
  "updated": "2020-05-23T13:38:43.000Z",
  "title": "Gelfand-Kirillov dimensions of simple highest weight modules for types BCD",
  "authors": [
    "Zhanqiang Bai",
    "Xun Xie"
  ],
  "comment": "25 pages. Comment welcome",
  "categories": [
    "math.RT",
    "math.CO"
  ],
  "abstract": "By using the Lusztig's $ \\mathbf{a} $-function, we give a combinatorial algorithm for Gelfand-Kirillov dimensions of simple highest weight modules of Lie algebras $ \\mathfrak{sp}_{2n} $, $ \\mathfrak{so}_{2n} $ and $ \\mathfrak{so}_{2n+1} $ in terms of their highest weights. Then we determine the associated varieties of highest weight Harish-Chandra modules of Lie groups $ Sp(2n,\\mathbb{R}) $, $ SO^*(2n) $, $ SO(2, 2n-1) $ and $ SO(2,2n-2) $ by computing their Gelfand-Kirillov dimensions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-23T13:38:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E47",
      "17B10",
      "20C08"
    ],
    "keywords": [
      "simple highest weight modules",
      "gelfand-kirillov dimensions",
      "types bcd",
      "highest weight harish-chandra modules",
      "lie algebras"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}