{
  "id": "2010.16112",
  "version": "v1",
  "published": "2020-10-30T08:07:05.000Z",
  "updated": "2020-10-30T08:07:05.000Z",
  "title": "Multiplicity one theorem for the unitary and orthogonal groups in positive characteristic",
  "authors": [
    "Dor Mezer"
  ],
  "comment": "16 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "In [AGRS] a multiplicity one theorem is proven for general linear groups, orthogonal groups and unitary groups ($GL, O$, and $U$) over $p$-adic local fields. That is to say that when we have a pair of such groups $G_n\\subseteq G_{n+1}$, any restriction of an irreducible smooth representation of $G_{n+1}$ to $G_n$ is multiplicity free. This property is already known for $GL$ over a local field of positive characteristic, and in this paper we also give a proof for $O,U$ over local fields of positive odd characteristic. By the Gelfand-Kazhdan criterion, this theorem reduces to the statement that any $G_n$-invariant distribution on $G_{n+1}$ is also invariant to transposition. This statement for $GL, O$, and $U$ over over $p$-adic local fields is proven in [AGRS]. An adaptation of the proof for $GL$ that works over of local fields of positive odd characteristic is given in [Mez]. In this paper we make this adaptation also for the orthogonal and unitary groups. Our methods are a synergy of the methods of [AGRS] and of [Mez].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-30T08:07:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E50",
      "20G05",
      "20G25",
      "46F10"
    ],
    "keywords": [
      "orthogonal groups",
      "positive characteristic",
      "adic local fields",
      "positive odd characteristic",
      "unitary groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}