{
  "id": "2410.04902",
  "version": "v1",
  "published": "2024-10-07T10:39:43.000Z",
  "updated": "2024-10-07T10:39:43.000Z",
  "title": "Unitary branching rules for the general linear Lie superalgebra",
  "authors": [
    "Mark Gould",
    "Yang Zhang"
  ],
  "comment": "14 pages",
  "categories": [
    "math.RT",
    "math-ph",
    "math.MP"
  ],
  "abstract": "In terms of highest weights, we establish branching rules for finite dimensional unitary simple modules of the general linear Lie superalgebra $\\mathfrak{gl}_{m|n}$. Our proof uses the Howe duality for $\\mathfrak{gl}_{m|n}$, as well as branching rules for Kac modules. Moreover, we derive the branching rules of type 2 unitary simple $\\mathfrak{gl}_{m|n}$-modules, which are dual to the aforementioned unitary modules.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-07T10:39:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B10",
      "05E10"
    ],
    "keywords": [
      "general linear lie superalgebra",
      "unitary branching rules",
      "finite dimensional unitary simple modules"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}