{
  "id": "1905.01321",
  "version": "v1",
  "published": "2019-05-03T18:00:43.000Z",
  "updated": "2019-05-03T18:00:43.000Z",
  "title": "Multiplicity one theorem for $(\\mathrm{GL}_{n+1},\\mathrm{GL}_n)$ over a local field of positive characteristic",
  "authors": [
    "Dor Mezer"
  ],
  "comment": "This article draws heavily from arXiv:0707.2363 by other author",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $\\mathbb{F}$ be a non-archimedean local field of positive characteristic different from 2. We consider distributions on $\\mathrm{GL}(n+1,\\mathbb{F})$ which are invariant under the adjoint action of $\\mathrm{GL}(n,\\mathbb{F})$. We prove that any such distribution is invariant with respect to transposition. This implies that the restriction to $\\mathrm{GL}(n,\\mathbb{F})$ of any irreducible smooth representation of $\\mathrm{GL}(n+1,\\mathbb{F})$ is multiplicity free.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-03T18:00:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E50",
      "20G05",
      "20G25",
      "46F10"
    ],
    "keywords": [
      "positive characteristic",
      "non-archimedean local field",
      "adjoint action",
      "multiplicity free",
      "irreducible smooth representation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}