{
  "id": "1808.10348",
  "version": "v1",
  "published": "2018-08-30T15:20:12.000Z",
  "updated": "2018-08-30T15:20:12.000Z",
  "title": "Discretely decomposable restrictions of $(\\mathfrak{g},K)$-modules for Klein four symmetric pairs of exceptional Lie groups of Hermitian type",
  "authors": [
    "Haian He"
  ],
  "comment": "7 pages, 1 figure",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $(G,G')$ be a Klein four symmetric pair. If $\\pi_K$ is a unitarizable simple $(\\mathrm{g},K)$-module, the author shows some necessary conditions when $\\pi_K$ is discretely decomposable as a $(\\mathfrak{g}',K')$-module. In particular, if $G$ is an exceptional Lie group of Hermitian type, i.e., $G=\\mathrm{E}_{6(-14)}$ or $\\mathrm{E}_{7(-25)}$, the author classifies all the Klein four symmetric pairs $(G,G')$ such that there exists at least one unitarizable simple $(\\mathfrak{g},K)$-module $\\pi_K$ that is discretely decomposable as a $(\\mathfrak{g}',K')$-module.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-30T15:20:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E46"
    ],
    "keywords": [
      "exceptional lie group",
      "symmetric pair",
      "discretely decomposable restrictions",
      "hermitian type",
      "unitarizable simple"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}