{
  "id": "1912.05294",
  "version": "v1",
  "published": "2019-12-11T13:39:02.000Z",
  "updated": "2019-12-11T13:39:02.000Z",
  "title": "On the symmetric Gelfand pair $(\\mathcal{H}_n\\times \\mathcal{H}_{n-1},diag (\\mathcal{H}_{n-1}))$",
  "authors": [
    "Omar Tout"
  ],
  "categories": [
    "math.CO",
    "math.RT"
  ],
  "abstract": "We show that the $\\mathcal{H}_{n-1}$-conjugacy classes of $\\mathcal{H}_n,$ where $\\mathcal{H}_n$ is the hyperoctahedral group on $2n$ elements, are indexed by marked bipartitions of $n.$ This will lead us to prove that $(\\mathcal{H}_n\\times \\mathcal{H}_{n-1},diag (\\mathcal{H}_{n-1}))$ is a symmetric Gelfand pair and that the induced representation $1_{diag (\\mathcal{H}_{n-1})}^{\\mathcal{H}_n\\times \\mathcal{H}_{n-1}}$ is multiplicity free.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-11T13:39:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E10",
      "05E15",
      "20C30"
    ],
    "keywords": [
      "symmetric gelfand pair",
      "multiplicity free",
      "conjugacy classes",
      "hyperoctahedral group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}