{
  "id": "1810.12053",
  "version": "v1",
  "published": "2018-10-29T11:01:33.000Z",
  "updated": "2018-10-29T11:01:33.000Z",
  "title": "Geodesic Normal Forms and Hecke Algebras for the Complex Reflection Groups G(de,e,n)",
  "authors": [
    "Georges Neaime"
  ],
  "categories": [
    "math.RT"
  ],
  "abstract": "We establish geodesic normal forms for the general series of complex reflection groups G(de,e,n) by using the presentations of Corran-Picantin and Corran-Lee-Lee of G(e,e,n) and G(de,e,n) for d > 1, respectively. This requires the elaboration of a combinatorial technique in order to explicitly determine minimal word representatives of the elements of G(de,e,n). Using these geodesic normal forms, we construct natural bases for the Hecke algebras associated with the complex reflection groups G(e,e,n) and G(d,1,n). As an application, we obtain a new proof of the BMR freeness conjecture for these groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-29T11:01:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "complex reflection groups",
      "geodesic normal forms",
      "hecke algebras",
      "explicitly determine minimal word representatives",
      "bmr freeness conjecture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}