{
  "id": "1406.1634",
  "version": "v2",
  "published": "2014-06-06T10:29:28.000Z",
  "updated": "2016-01-08T17:18:57.000Z",
  "title": "The notion of cusp forms for a class of reductive symmetric spaces of split rank one",
  "authors": [
    "Erik P. van den Ban",
    "Job J. Kuit",
    "Henrik Schlichtkrull"
  ],
  "comment": "41 pages. Mostly minor changes to improve exposition. Major simplification of the proof of Theorem 6.1 in Section 6.2",
  "categories": [
    "math.RT"
  ],
  "abstract": "We study a notion of cusp forms for the symmetric spaces G/H with G = SL(n,R) and H = S(GL(n-1,R) x GL(1,R)). We classify all minimal parabolic subgroups of G for which the associated cuspidal integrals are convergent and discuss the possible definitions of cusp forms. Finally, we show that the closure of the direct sum of the discrete series of representations of G/H coincides with the space of cusp forms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-06-06T10:29:28.000Z",
      "comment": "37 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2016-01-08T17:18:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E30",
      "22E45"
    ],
    "keywords": [
      "cusp forms",
      "reductive symmetric spaces",
      "split rank",
      "minimal parabolic subgroups",
      "symmetric spaces g/h"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 41,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1406.1634V"
    }
  }
}