{
  "id": "2108.02617",
  "version": "v1",
  "published": "2021-08-05T13:52:16.000Z",
  "updated": "2021-08-05T13:52:16.000Z",
  "title": "On semisimplicity of Jantzen middles for the periplectic Lie superalgebra",
  "authors": [
    "Chih-Whi Chen"
  ],
  "comment": "18 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "We prove that an integral block of the category $\\mathcal O$ of the periplectic Lie superalgebra contains a non-semisimple Jantzen middle if and only if it contains a simple module of atypical highest weight. As a consequence, every atypical integral block of $\\mathcal O$ does not admit a Kazhdan-Lusztig theory in the sense of Cline, Parshall and Scott.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-05T13:52:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10",
      "17B55"
    ],
    "keywords": [
      "semisimplicity",
      "periplectic lie superalgebra contains",
      "non-semisimple jantzen middle",
      "kazhdan-lusztig theory",
      "simple module"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}