{
  "id": "2002.12864",
  "version": "v1",
  "published": "2020-02-28T17:00:22.000Z",
  "updated": "2020-02-28T17:00:22.000Z",
  "title": "$C^\\ast$-blocks and crossed products for classical $p$-adic groups",
  "authors": [
    "Alexandre Afgoustidis",
    "Anne-Marie Aubert"
  ],
  "comment": "35 pages",
  "categories": [
    "math.RT",
    "math.OA"
  ],
  "abstract": "Let $G$ be a real or $p$-adic reductive group. We consider the tempered dual of $G$, and its connected components. For real groups, Wassermann proved in 1987, by noncommutative-geometric methods, that each connected component has a simple geometric structure which encodes the reducibility of induced representations. For $p$-adic groups, each connected component of the tempered dual comes with a compact torus equipped with a finite group action, and we prove that a version of Wassermann's theorem holds true under a certain geometric assumption on the structure of stabilizers for that action. We then focus on the case where $G$ is a quasi-split symplectic, orthogonal or unitary group, and explicitly determine the connected components for which the geometric assumption is satisfied.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-28T17:00:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E50",
      "22D25"
    ],
    "keywords": [
      "adic groups",
      "connected component",
      "crossed products",
      "wassermanns theorem holds true",
      "geometric assumption"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}