{
  "id": "2007.09778",
  "version": "v1",
  "published": "2020-07-19T20:34:11.000Z",
  "updated": "2020-07-19T20:34:11.000Z",
  "title": "Normal Reflection Subgroups of Complex Reflection Groups",
  "authors": [
    "Carlos E. Arreche",
    "Nathan F. Williams"
  ],
  "categories": [
    "math.CO",
    "math.RT"
  ],
  "abstract": "We study normal reflection subgroups of complex reflection groups. Our approach leads to a refinement of a theorem of Orlik and Solomon to the effect that the generating function for fixed-space dimension over a reflection group is a product of linear factors involving generalized exponents. Our refinement gives a uniform proof and generalization of a recent theorem of the second author.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-19T20:34:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F55",
      "05E10"
    ],
    "keywords": [
      "complex reflection groups",
      "study normal reflection subgroups",
      "refinement",
      "fixed-space dimension",
      "linear factors"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}