{
  "id": "1807.11833",
  "version": "v1",
  "published": "2018-07-31T14:19:30.000Z",
  "updated": "2018-07-31T14:19:30.000Z",
  "title": "On the spectral gap of some Cayley graphs on the Weyl group $W(B_n)$",
  "authors": [
    "Filippo Cesi"
  ],
  "comment": "17 pages",
  "categories": [
    "math.CO",
    "math.GR",
    "math.PR"
  ],
  "abstract": "The Laplacian of a (weighted) Cayley graph on the Weyl group $W(B_n)$ is a $N\\times N$ matrix with $N = 2^n n!$ equal to the order of the group. We show that for a class of (weighted) generating sets, its spectral gap (lowest nontrivial eigenvalue), is actually equal to the spectral gap of a $2n \\times 2n$ matrix associated to a $2n$-dimensional permutation representation of $W_n$. This result can be viewed as an extension to $W(B_n)$ of an analogous result valid for the symmetric group, known as `Aldous' spectral gap conjecture', proven in 2010 by Caputo, Liggett and Richthammer.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-31T14:19:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C25",
      "05C50",
      "20C15",
      "20C30",
      "60K35"
    ],
    "keywords": [
      "weyl group",
      "cayley graph",
      "dimensional permutation representation",
      "lowest nontrivial eigenvalue",
      "spectral gap conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}