{
  "id": "1405.6023",
  "version": "v1",
  "published": "2014-05-23T11:12:30.000Z",
  "updated": "2014-05-23T11:12:30.000Z",
  "title": "Multiplicity formula for restriction of representations of $\\widetilde{\\rm GL}_{2}(E)$ to $\\widetilde{\\rm SL}_{2}(E)$",
  "authors": [
    "Shiv Prakash Patel",
    "Dipendra Prasad"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "In this note we prove a certain multiplicity formula regarding the restriction of an irreducible admissible genuine representation of a 2-fold cover $\\widetilde{{\\rm GL}}_{2}(E)$ of ${\\rm GL}_{2}(E)$ to the 2-fold cover $\\widetilde{{\\rm SL}}_{2}(E)$ of ${\\rm SL}_{2}(E)$, and find in particular that this multiplicity may not be one, a result that seems to have been noticed before. The proofs follow the standard path via Waldspurger's analysis of theta correspondence between $\\widetilde{{\\rm SL}}_{2}(E)$ and ${\\rm PGL}_{2}(E)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-05-23T11:12:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E35",
      "22E50"
    ],
    "keywords": [
      "restriction",
      "irreducible admissible genuine representation",
      "standard path",
      "waldspurgers analysis",
      "theta correspondence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}