{
  "id": "1711.08635",
  "version": "v1",
  "published": "2017-11-23T10:08:11.000Z",
  "updated": "2017-11-23T10:08:11.000Z",
  "title": "The infinitesimal characters of discrete series for real spherical spaces",
  "authors": [
    "Bernhard Krötz",
    "Job J. Kuit",
    "Eric M. Opdam",
    "Henrik Schlichtkrull"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $Z=G/H$ be the homogeneous space of a real reductive group and a unimodular real spherical subgroup, and consider the regular representation of $G$ on $L^2(Z)$. It is shown that all representations of the discrete series, that is, the irreducible subrepresentations of $L^2(Z)$, have infinitesimal characters which are real and belong to a lattice. Moreover, let $K$ be a maximal compact subgroup of $G$. Then each irreducible representation of $K$ occurs in a finite set of such discrete series representations only. Similar results are obtained for the twisted discrete series, that is, the discrete components of the space of square integrable sections of a line bundle, given by a unitary character on an abelian extension of $H$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-23T10:08:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "real spherical spaces",
      "infinitesimal characters",
      "discrete series representations",
      "unimodular real spherical subgroup",
      "maximal compact subgroup"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}