{
  "id": "1908.04723",
  "version": "v1",
  "published": "2019-08-13T16:30:53.000Z",
  "updated": "2019-08-13T16:30:53.000Z",
  "title": "On the branching rules for Klein four symmetric pairs",
  "authors": [
    "Haian HE"
  ],
  "comment": "9 pages, 1 figure",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $G$ be an exceptional simple Lie group of Hermitian type, i.e., $G=\\mathrm{E}_{6(-14)}$ or $\\mathrm{E}_{7(-25)}$, and $(G,G^\\Gamma)$ a Klein four symmetric pair. In this paper, firstly, the author shows that there exists a discrete series representation $\\pi$ of $G$ which is $G^\\Gamma$-admissible if and only if $(G,G^\\Gamma)$ is of holomorphic type. Secondly, the author discusses the discretely decomposable restrictions of $(\\mathfrak{g},K)$-modules for the case when $G^\\Gamma$ is compact. Finally, the author studies a conjecture by Toshiyuki KOBAYASHI for the associated varieties, and confirms the conjecture for certain pairs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-13T16:30:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E46"
    ],
    "keywords": [
      "symmetric pair",
      "branching rules",
      "exceptional simple lie group",
      "discrete series representation",
      "author studies"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}