{
  "id": "2408.01856",
  "version": "v1",
  "published": "2024-08-03T19:47:02.000Z",
  "updated": "2024-08-03T19:47:02.000Z",
  "title": "On Speh representations for level zero supercuspidal representations and Ginzburg-Kaplan gamma factors",
  "authors": [
    "Elad Zelingher"
  ],
  "comment": "42 pages. Comments are welcome!",
  "categories": [
    "math.RT",
    "math.NT"
  ],
  "abstract": "We establish a relation between Speh representations of $\\mathrm{GL}_n\\left(\\mathbb{F}_q\\right)$ and Speh representations of $\\mathrm{GL}_n\\left(F\\right)$, where $F$ is a non-archimedean local field. We use irreducible level zero supercuspidal representations to show that these two notions of Speh representations associated to cuspidal representations are related via a commutative diagram, and that their corresponding $(k,c)$ $\\psi$-Whittaker models are also related. We use these results to relate the local Ginzburg-Kaplan integrals for level zero supercuspidal representations to their finite field counterparts.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-03T19:47:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F70",
      "11F66",
      "20C33",
      "22E50"
    ],
    "keywords": [
      "speh representations",
      "ginzburg-kaplan gamma factors",
      "irreducible level zero supercuspidal representations",
      "non-archimedean local field",
      "finite field counterparts"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 42,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}