{
  "id": "1405.2431",
  "version": "v2",
  "published": "2014-05-10T13:26:05.000Z",
  "updated": "2015-11-13T20:40:17.000Z",
  "title": "Weyl calculus and dual pairs",
  "authors": [
    "M. McKee",
    "A. Pasquale",
    "T. Przebinda"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "We consider a dual pair $(G,G')$, in the sense of Howe, with $G$ compact acting on $L^2(\\mathbb R^n)$ for an appropriate $n$ via the Weil Representation. Let $\\widetilde{G}$ be the preimage of $G$ in the metaplectic group. Given a genuine irreducible unitary representation $\\Pi$ of $\\widetilde{G}$ we compute the Weyl symbol of orthogonal projection onto $L^2(\\mathbb R^n)_\\Pi$, the $\\Pi$-isotypic component. We apply the result to obtain an explicit formula for the character of the corresponding irreducible unitary representation $\\Pi'$ of $\\widetilde{G'}$ and to compute of the wave front set of $\\Pi'$ by elementary means.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-05-10T13:26:05.000Z",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-11-13T20:40:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E45",
      "22E46",
      "22E30"
    ],
    "keywords": [
      "dual pair",
      "weyl calculus",
      "genuine irreducible unitary representation",
      "wave front set",
      "elementary means"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.2431M"
    }
  }
}