{
  "id": "1406.3738",
  "version": "v1",
  "published": "2014-06-14T14:33:15.000Z",
  "updated": "2014-06-14T14:33:15.000Z",
  "title": "Covers of tori over local and global fields",
  "authors": [
    "Martin H. Weissman"
  ],
  "comment": "34 pages",
  "categories": [
    "math.RT",
    "math.NT"
  ],
  "abstract": "Langlands has described the irreducible admissible representations of $T$, when $T$ is the group of points of an algebraic torus over a local field. Also, Langlands described the automorphic representations of $T_{\\mathbb A}$ when $T_{\\mathbb A}$ is the group of adelic points of an algebraic torus over a global field $F$. We describe irreducible (in the local setting) and automorphic (in the global setting) $\\epsilon$-genuine representations for covers of tori, also known as metaplectic tori, which arise from a framework of Brylinski and Deligne. In particular, our results include a description of spherical Hecke algebras in the local unramified setting, and a global multiplicity estimate for automorphic representations of covers of split tori. For automorphic representations of covers of split tori, we prove a multiplicity-one theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-06-14T14:33:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F70",
      "22E50",
      "22E55"
    ],
    "keywords": [
      "global field",
      "automorphic representations",
      "algebraic torus",
      "split tori",
      "global multiplicity estimate"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1406.3738W"
    }
  }
}