{
  "id": "1702.05836",
  "version": "v1",
  "published": "2017-02-20T02:23:44.000Z",
  "updated": "2017-02-20T02:23:44.000Z",
  "title": "The socle filtrations of principal series representations of $SL(3,\\mathbb{R})$ and $Sp(2,\\mathbb{R})$",
  "authors": [
    "Naoki Hashimoto",
    "Kenji Taniguchi",
    "Go Yamanaka"
  ],
  "comment": "46 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "We study the structure of the $(\\mathfrak{g},K)$-modules of the principal series representations of $SL(3,\\mathbb{R})$ and $Sp(2,\\mathbb{R})$ induced from minimal parabolic subgroups, in the case when the infinitesimal character is nonsingular. The composition factors of these modules are known by Kazhdan-Lusztig-Vogan conjecture. In this paper, we give complete descriptions of the socle filtrations of these modules.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-20T02:23:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E46"
    ],
    "keywords": [
      "principal series representations",
      "socle filtrations",
      "minimal parabolic subgroups",
      "composition factors",
      "complete descriptions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 46,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}