{
  "id": "1209.2798",
  "version": "v2",
  "published": "2012-09-13T07:28:54.000Z",
  "updated": "2012-09-22T08:07:45.000Z",
  "title": "Self-dual representations with vectors fixed under an Iwahori subgroup",
  "authors": [
    "Kumar Balasubramanian"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $G$ be the group of $F$-points of a split connected reductive $F$-group over a non-Archimedean local field $F$ of characteristic 0. Let $\\pi$ be an irreducible smooth self-dual representation of $G$. The space $W$ of $\\pi$ carries a non-degenerate $G$-invariant bilinear form $(\\,,\\,)$ which is unique up to scaling. The form is easily seen to be symmetric or skew-symmetric and we set $\\varepsilon({\\pi})=\\pm 1$ accordingly. In this article, we show that $\\varepsilon{(\\pi)}=1$ when $\\pi$ is a generic representation of $G$ with non-zero vectors fixed under an Iwahori subgroup $I$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-09-22T08:07:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "iwahori subgroup",
      "invariant bilinear form",
      "irreducible smooth self-dual representation",
      "non-archimedean local field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1209.2798B"
    }
  }
}