{
  "id": "2109.00204",
  "version": "v1",
  "published": "2021-09-01T06:12:54.000Z",
  "updated": "2021-09-01T06:12:54.000Z",
  "title": "Finite multiplicities beyond spherical pairs",
  "authors": [
    "Avraham Aizenbud",
    "Dmitry Gourevitch"
  ],
  "comment": "22p. Appendix B by Ido Krashon",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $G$ be a real reductive algebraic group, and let $H\\subset G$ be an algebraic subgroup. It is known that the action of $G$ on the space of functions on $G/H$ is \"tame\" if this space is spherical. In particular, the multiplicities of the space $\\mathcal{S}(G/H)$ of Schwartz functions on $G/H$ are finite in this case. In this paper we formulate and analyze a generalization of sphericity that implies finite multiplicities in $\\mathcal{S}(G/H)$ for small enough irreducible representations of $G$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-09-01T06:12:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20G05",
      "14L30",
      "22E46",
      "22E47",
      "22E45"
    ],
    "keywords": [
      "spherical pairs",
      "implies finite multiplicities",
      "real reductive algebraic group",
      "schwartz functions",
      "algebraic subgroup"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}