{
  "id": "1507.01042",
  "version": "v1",
  "published": "2015-07-03T22:19:54.000Z",
  "updated": "2015-07-03T22:19:54.000Z",
  "title": "L-groups and parameters for covering groups",
  "authors": [
    "Martin H. Weissman"
  ],
  "comment": "140 pages, This article supersedes arXiv:1501.06169",
  "categories": [
    "math.NT",
    "math.RT"
  ],
  "abstract": "We incorporate covers of quasisplit reductive groups into the Langlands program, defining an L-group associated to such a cover. We work with all covers that arise from extensions of quasisplit reductive groups by $\\mathbf{K}_2$ -- the class studied by Brylinski and Deligne. We use this L-group to parameterize genuine irreducible representations in many contexts, including covers of split tori, unramified representations, and discrete series for double covers of semisimple groups over $\\mathbb R$. An appendix surveys torsors and gerbes on the \\'etale site, as they are used in the construction of the L-group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-03T22:19:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F70",
      "22E50",
      "22E55"
    ],
    "keywords": [
      "covering groups",
      "quasisplit reductive groups",
      "parameters",
      "appendix surveys torsors",
      "etale site"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 140,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150701042W"
    }
  }
}