{
  "id": "1902.02018",
  "version": "v1",
  "published": "2019-02-06T04:25:04.000Z",
  "updated": "2019-02-06T04:25:04.000Z",
  "title": "Restriction of $p$-modular representations of $U(2, 1)$ to a Borel subgroup",
  "authors": [
    "Peng Xu"
  ],
  "comment": "Preliminary version, comments welcome",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $G$ be the unramified unitary group $U(2, 1)(E/F)$ defined over a non-archimedean local field $F$ of odd residue characteristic $p$, and $B$ be the standard Borel subgroup of $G$. We prove in this note that the restriction of any supersingular representation of $G$ to $B$ is irreducible, analogous to a result of Pa$\\check{\\text{s}}$k$\\bar{\\text{u}}$nas on $GL_2 (F)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-06T04:25:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E50"
    ],
    "keywords": [
      "modular representations",
      "restriction",
      "odd residue characteristic",
      "non-archimedean local field",
      "standard borel subgroup"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}