{
  "id": "1502.07392",
  "version": "v1",
  "published": "2015-02-25T22:51:11.000Z",
  "updated": "2015-02-25T22:51:11.000Z",
  "title": "Spectra of Cayley Graphs of Complex Reflection Groups",
  "authors": [
    "Briana Foster-Greenwood",
    "Cathy Kriloff"
  ],
  "comment": "30 pages, 11 tables",
  "categories": [
    "math.CO",
    "math.GR",
    "math.RT"
  ],
  "abstract": "Renteln proved that the eigenvalues of the distance matrix of a Cayley graph of a real reflection group with respect to the set of all reflections are integral and provided a combinatorial formula for such spectra. We prove the eigenvalues of the distance, adjacency, and codimension matrices of Cayley graphs of complex reflection groups with connection sets consisting of all reflections are integral and provide a combinatorial formula for the codimension spectra for the monomial complex reflection groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-02-25T22:51:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C50",
      "20F55",
      "05C25"
    ],
    "keywords": [
      "cayley graph",
      "combinatorial formula",
      "monomial complex reflection groups",
      "real reflection group",
      "distance matrix"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150207392F"
    }
  }
}