{
  "id": "0909.1227",
  "version": "v2",
  "published": "2009-09-07T12:03:02.000Z",
  "updated": "2010-08-30T21:26:47.000Z",
  "title": "Analytic R-groups of affine Hecke algebras",
  "authors": [
    "Eric Opdam",
    "Patrick Delorme"
  ],
  "comment": "Some improvements in the presentation were made, and an example has been added showing the nontriviality of the cohomology class of the 2-cocycle $\\gamma_\\Delta$ (as opposed to $\\gamma$ itself) for Hecke algebras of type D",
  "categories": [
    "math.RT"
  ],
  "abstract": "We define analytic $R$-groups for affine Hecke algebras, and prove the analog of the Knapp-Stein Dimension Theorem. As a corollary we prove that the commutant algebra of a unitary principal series representation is isomorphic to the complex group algebra of the $R$-group, twisted by a certain 2-cocycle $\\gamma$. For classical Hecke algebras we prove that $\\gamma$ is always trivial.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-08-30T21:26:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C08",
      "22D25",
      "22E35",
      "43A40"
    ],
    "keywords": [
      "affine hecke algebras",
      "analytic r-groups",
      "unitary principal series representation",
      "knapp-stein dimension theorem",
      "complex group algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0909.1227O"
    }
  }
}