{
  "id": "2208.02308",
  "version": "v1",
  "published": "2022-08-03T18:47:26.000Z",
  "updated": "2022-08-03T18:47:26.000Z",
  "title": "Fourier-Jacobi models of Deligne-Lusztig characters and depth zero local descent for unitary groups",
  "authors": [
    "Dongwen Liu",
    "Jia-Jun Ma",
    "Fang Shi"
  ],
  "comment": "31 pages. Comments are welcome",
  "categories": [
    "math.RT",
    "math.NT"
  ],
  "abstract": "In this paper, we deduce explicit multiplicity formulas of the Fourier-Jacobi model for Deligne-Lusztig characters of finite symplectic groups, unitary groups, and general linear groups. We then apply these results to deduce the explicit depth zero local descent (\\`a la Soudry and Tanay) for $p$-adic unitary groups. The result is a concrete example in the context of non-tempered Gan-Gross-Prasad program.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-03T18:47:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "unitary groups",
      "deligne-lusztig characters",
      "fourier-jacobi model",
      "explicit depth zero local descent",
      "deduce explicit multiplicity formulas"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}