{
  "id": "1402.1717",
  "version": "v2",
  "published": "2014-02-07T17:44:55.000Z",
  "updated": "2014-09-22T15:33:18.000Z",
  "title": "Invariant differential operators on H-type groups and discrete components in restrictions of complementary series of rank one semisimple groups",
  "authors": [
    "Jan Möllers",
    "Bent Ørsted",
    "Genkai Zhang"
  ],
  "comment": "22 pages; added Section 5 in v2 to separate H-type results and rank one results",
  "doi": "10.1007/s12220-014-9540-z",
  "categories": [
    "math.RT"
  ],
  "abstract": "We explicitly construct a finite number of discrete components in the restriction of complementary series representations of rank one semisimple groups $G$ to rank one subgroups $G_1$. For this we use the realizations of complementary series representations of $G$ and $G_1$ on Sobolev spaces on the nilpotent radicals $N$ and $N_1$ of the minimal parabolics in $G$ and $G_1$, respectively. The groups $N$ and $N_1$ are of H-type and we construct explicitly invariant differential operators between $N$ and $N_1$. These operators induce the projections onto the discrete components. Our construction of the invariant differential operators is carried out uniformly in the framework of H-type groups and also works for those H-type groups which do not occur as nilpotent radical of a parabolic subgroup in a semisimple group.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-02-07T17:44:55.000Z",
      "comment": "20 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-09-22T15:33:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E46",
      "22E25"
    ],
    "keywords": [
      "h-type groups",
      "semisimple group",
      "discrete components",
      "complementary series representations",
      "restriction"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1402.1717M"
    }
  }
}