{
  "id": "math/0610156",
  "version": "v1",
  "published": "2006-10-04T18:12:07.000Z",
  "updated": "2006-10-04T18:12:07.000Z",
  "title": "On the restriction of representations of $\\GL_2(F)$ to a Borel subgroup",
  "authors": [
    "Vytautas Paskunas"
  ],
  "comment": "17 pages",
  "categories": [
    "math.RT",
    "math.NT"
  ],
  "abstract": "Let $F$ be a non-Archimedean local field and let $p$ be the residual characteristic of $F$. Let $G=GL_2(F)$ and let $P$ be a Borel subgroup of $G$. In this paper we study the restriction of irreducible representations of $G$ on $E$-vector spaces to $P$, where $E$ is an algebraically closed field of characteristic $p$. We show that in a certain sense $P$ controls the representation theory of $G$. We then extend our results to smooth $\\oK[G]$- modules of finite length and unitary $K$-Banach space representations of $G$, where $\\oK$ is the ring of integers of a complete discretely valued field $K$, with residue field $E$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-10-04T18:12:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E50"
    ],
    "keywords": [
      "borel subgroup",
      "restriction",
      "banach space representations",
      "non-archimedean local field",
      "residue field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....10156P"
    }
  }
}