{
  "id": "1610.06441",
  "version": "v1",
  "published": "2016-10-20T14:42:29.000Z",
  "updated": "2016-10-20T14:42:29.000Z",
  "title": "Self-dual representations of Sp(4,F)",
  "authors": [
    "Kumar Balasubramanian"
  ],
  "comment": "This is a preliminary version. Any comments and suggestions will be appreciated",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $F$ be a non-Archimedean local field of characteristic $0$ and $G=Sp(4,F)$. Let $(\\pi,W)$ be an irreducible smooth self-dual representation $G$. The space $W$ of $\\pi$ admits 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 paper, we show that $\\varepsilon{(\\pi)}=1$ when $\\pi$ is an Iwahori spherical representation of $G$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-20T14:42:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "non-archimedean local field",
      "irreducible smooth self-dual representation",
      "invariant bilinear form",
      "iwahori spherical representation",
      "non-degenerate"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}