{
  "id": "2001.08186",
  "version": "v1",
  "published": "2020-01-22T18:11:38.000Z",
  "updated": "2020-01-22T18:11:38.000Z",
  "title": "Doubling Constructions: the complete L-function for coverings of the symplectic group",
  "authors": [
    "Eyal Kaplan"
  ],
  "categories": [
    "math.NT",
    "math.RT"
  ],
  "abstract": "We develop the local theory of the generalized doubling method for the $m$-fold central extension $Sp_{2n}^{(m)}$ of Matsumoto of the symplectic group. We define local $\\gamma$-, $L$- and $\\epsilon$-factors for pairs of genuine representations of $Sp_{2n}^{(m)}\\times\\widetilde{GL}_k$ and prove their fundamental properties, in the sense of Shahidi. Here $\\widetilde{GL}_k$ is the central extension of $GL_k$ arising in the context of the Langlands--Shahidi method for covering groups of $Sp_{2n}\\times GL_k$. We then construct the complete $L$-function for cuspidal representations and prove its global functional equation. Possible applications include classification results and a Shimura type lift of representations from covering groups to general linear groups (a global lift is sketched here for $m=2$).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-22T18:11:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F70",
      "11F55",
      "11F66",
      "22E50",
      "22E55"
    ],
    "keywords": [
      "symplectic group",
      "complete l-function",
      "doubling constructions",
      "shimura type lift",
      "representations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}