{
  "id": "math/9909023",
  "version": "v1",
  "published": "1999-09-03T09:58:06.000Z",
  "updated": "1999-09-03T09:58:06.000Z",
  "title": "Harmonic Analysis on the quotient $\\Q^\\times\\ltimes\\Q\\bs\\A^1\\ltimes \\A$",
  "authors": [
    "Anton Deitmar"
  ],
  "comment": "LATEX, 11 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $G$ be the semidirect product $\\A^1\\ltimes \\A$ of the adeles and the norm 1 ideles. Let $\\Ga$ be the discrete subgroup $\\Q^\\times\\ltimes\\Q$. In this paper the trace formula for this setting is established and used to give the complete decomposition of the $G$-representation on $L^2(\\Ga\\bs G)$. It turns out that every character of the norm-1 idele class group gives a one dimensional isotype and the complement of those consists of one irreducible representation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1999-09-03T09:58:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "harmonic analysis",
      "idele class group",
      "semidirect product",
      "complete decomposition",
      "discrete subgroup"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math......9023D"
    }
  }
}