{
  "id": "2405.06450",
  "version": "v1",
  "published": "2024-05-10T13:02:10.000Z",
  "updated": "2024-05-10T13:02:10.000Z",
  "title": "On the Jacquet functor of Symplectic groups",
  "authors": [
    "Prem Dagar",
    "Mahendra Kumar Verma"
  ],
  "comment": "12 pages; comments are welcome. arXiv admin note: text overlap with arXiv:2405.05719",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $\\F$ be a non-Archimedean local field.~Consider $\\G_{n}:= \\Sp_{2n}(\\F)$ and let $\\M:= \\GL_l \\times \\G_{n-l}$ be a maximal Levi subgroup of $\\G_{n}$.~This paper undertakes the computation of the Jacquet module of representations of $\\G_{n}$ with respect to the maximal Levi subgroup, belonging to a particular class. Finally, we conclude that for a subclass of representations of $\\G_{n},$ multiplicity of the Jacquet module does not exceed 2.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-10T13:02:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G05",
      "20C30",
      "20C33",
      "46F10",
      "47A67"
    ],
    "keywords": [
      "symplectic groups",
      "jacquet functor",
      "maximal levi subgroup",
      "jacquet module",
      "non-archimedean local"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}