{
  "id": "2012.01200",
  "version": "v1",
  "published": "2020-12-02T13:34:51.000Z",
  "updated": "2020-12-02T13:34:51.000Z",
  "title": "On the distinction of Iwahori-spherical representations",
  "authors": [
    "Paul Broussous"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $E/F$ be a quadratic unramified extension of non-archimedean local fields and $\\mathbb H$ a simply connected semisimple algebraic group defined and split over $F$. We establish general results (multiplicities, test vectors) on $\\HH (F)$-distinguished Iwahori-spherical representations of $\\HH (E)$. For discrete series Iwahori-spherical representations of $\\HH (E)$, we prove a numerical criterion of $\\HH (F)$-distinction. As an application, we classify the $\\HH (F)$-distinguished discrete series representations of $\\HH (E)$ corresponding to degree $1$ characters of the Iwahori-Hecke algebra.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-02T13:34:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "distinction",
      "non-archimedean local fields",
      "distinguished discrete series representations",
      "simply connected semisimple algebraic group",
      "discrete series iwahori-spherical representations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}