{
  "id": "math/9811189",
  "version": "v1",
  "published": "1998-11-01T00:00:00.000Z",
  "updated": "1998-11-01T00:00:00.000Z",
  "title": "On the classification of unitary representations of reductive Lie groups",
  "authors": [
    "Susana A. Salamanca-Riba",
    "David A. Vogan Jr."
  ],
  "comment": "67 pages, published version, abstract added in migration",
  "journal": "Ann. of Math. (2) 148 (1998), no. 3, 1067-1133",
  "categories": [
    "math.RT"
  ],
  "abstract": "Suppose G is a real reductive Lie group in Harish-Chandra's class. We propose here a structure for the set \\Pi_u(G) of equivalence classes of irreducible unitary representations of G. (The subscript u will be used throughout to indicate structures related to unitary representations.) We decompose \\Pi_{u}(G) into disjoint subsets with a (very explicit) discrete parameter set \\Lambda_u: \\Pi_u(G) = \\bigcup_{\\lambda_u \\in \\Lambda_u} \\Pi_u^{\\lambda_u}(G). Each subset is identified conjecturally with a collection of unitary representations of a certain subgroup G(\\lambda_u) of G. (We will give strong evidence and partial results for this conjecture.) In this way the problem of classifying \\Pi_u(G) would be reduced (by induction on the dimension of G) to the case G(\\lambda_u) = G.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1998-11-01T00:00:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "classification",
      "real reductive lie group",
      "discrete parameter set",
      "partial results",
      "equivalence classes"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Princeton University and the Institute for Advanced Study",
      "journal": "Ann. Math."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 67,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998math.....11189S"
    }
  }
}