{
  "id": "2010.14975",
  "version": "v1",
  "published": "2020-10-28T13:36:47.000Z",
  "updated": "2020-10-28T13:36:47.000Z",
  "title": "Semisimplicity of the $DS$ functor for the orthosymplectic Lie superalgebra",
  "authors": [
    "Maria Gorelik",
    "Thorsten Heidersdorf"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "We prove that the Duflo-Serganova functor $DS_x$ attached to an odd nilpotent element $x$ of $\\mathfrak{osp}(m|2n)$ is semisimple, i.e. sends a semisimple representation $M$ of $\\mathfrak{osp}(m|2n)$ to a semisimple representation of $\\mathfrak{osp}(m-2k|2n-2k)$ where $k$ is the rank of $x$. We prove a closed formula for $DS_x(L(\\lambda))$ in terms of the arc diagram attached to $\\lambda$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-28T13:36:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10",
      "17B20",
      "17B55",
      "18D10"
    ],
    "keywords": [
      "orthosymplectic lie superalgebra",
      "semisimplicity",
      "semisimple representation",
      "odd nilpotent element",
      "duflo-serganova functor"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}