{
  "id": "2210.13155",
  "version": "v1",
  "published": "2022-10-24T12:15:08.000Z",
  "updated": "2022-10-24T12:15:08.000Z",
  "title": "Centralizers of nilpotent elements in basic classical Lie superalgebras in good characteristic",
  "authors": [
    "Leyu Han"
  ],
  "comment": "23 pages, 18 figures",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let \\mathfrak{g}=\\mathfrak{g}_{\\bar{0}}\\oplus\\mathfrak{g}_{\\bar{1}} be a basic classical Lie superalgebra over an algebraically closed field \\mathbb{K} whose characteristic p>0 is a good prime for \\mathfrak{g}. Let G_{\\bar{0}} be the reductive algebraic group over \\mathbb{K} such that \\mathrm{Lie}(G_{\\bar{0}})=\\mathfrak{g}_{\\bar{0}}. Suppose e\\in\\mathfrak{g}_{\\bar{0}} is nilpotent. Write \\mathfrak{g}^{e} for the centralizer of e in \\mathfrak{g} and \\mathfrak{z}(\\mathfrak{g}^{e}) for the centre of \\mathfrak{g}^{e}. We calculate a basis for \\mathfrak{g}^{e} and \\mathfrak{z}(\\mathfrak{g}^{e}) by using associated cocharacters \\tau:\\mathbb{K}^{\\times}\\rightarrow G_{\\bar{0}} of e. In addition, we give the classification of e which are reachable, strongly reachable or satisfy the Panyushev property for exceptional Lie superalgebras D(2,1;\\alpha), G(3) and F(4).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-24T12:15:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B05",
      "17B20",
      "17B22",
      "17B25"
    ],
    "keywords": [
      "basic classical lie superalgebra",
      "nilpotent elements",
      "centralizer",
      "characteristic",
      "exceptional lie superalgebras"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}