{
  "id": "2205.07262",
  "version": "v1",
  "published": "2022-05-15T11:29:26.000Z",
  "updated": "2022-05-15T11:29:26.000Z",
  "title": "Multiplicity-free representations of certain nilpotent Lie groups over Siegel domains of the second kind",
  "authors": [
    "Koichi Arashi"
  ],
  "comment": "17 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "We investigate the multiplicity-freeness property of holomorphic multiplier representations of an affine transformation group on a Siegel domain of the second kind. We first deal with a generalized Heisenberg group. Next, for a certain smaller group, we give some necessary and sufficient conditions for the representation defined by the trivial multiplier to be multiplicity-free. We relate the multiplicity-freeness property to the coisotropicity and the visibility of the group action and to the commutativity of the algebra of invariant differential operators.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-15T11:29:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E27",
      "32M05",
      "53C55"
    ],
    "keywords": [
      "nilpotent lie groups",
      "siegel domain",
      "second kind",
      "multiplicity-free representations",
      "multiplicity-freeness property"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}