{
  "id": "1812.03033",
  "version": "v1",
  "published": "2018-12-07T14:23:06.000Z",
  "updated": "2018-12-07T14:23:06.000Z",
  "title": "Central morphisms and Cuspidal automorphic Representations",
  "authors": [
    "Jean-Pierre Labesse",
    "Joachim Schwermer"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $F$ be a global field. Let $G$ and $H$ be two connected reductive group defined over $F$ endowed with an $F$-morphism $f: H\\rightarrow G$ such that the induced morphism $H_{der}\\rightarrow G_{der}$ on the derived groups is a central isogeny. Our main results yield in particular the following theorem: Given any irreducible cuspidal representation $\\pi$ of $G(\\mathbb A_F)$ its restriction to $H(\\mathbb A_F)$ contains a cuspidal representation $\\sigma$ of $H(\\mathbb A_F)$. Conversely, assuming moreover that $f$ is an injection, any irreducible cuspidal representation $\\sigma$ of $H(\\mathbb A_F)$ appears in the restriction of some cuspidal representation $\\pi$ of $G(\\mathbb A_F)$. This theorem has an obvious local analogue.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-07T14:23:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cuspidal automorphic representations",
      "central morphisms",
      "irreducible cuspidal representation",
      "main results yield",
      "global field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}