{
  "id": "1608.00834",
  "version": "v1",
  "published": "2016-08-02T14:23:45.000Z",
  "updated": "2016-08-02T14:23:45.000Z",
  "title": "The Broué-Malle-Rouquier conjecture for the exceptional groups of rank 2",
  "authors": [
    "Eirini Chavli"
  ],
  "comment": "PhD thesis, 12 May 2016",
  "categories": [
    "math.RT"
  ],
  "abstract": "Between 1994 and 1998, the work of M. Brou\\'e, G. Malle, and R. Rouquier generalized in a natural way the definition of the Hecke algebra associated to a finite Coxeter group, for the case of an arbitrary complex reflection group. Attempting to also generalize the properties of the Coxeter case, they stated a number of conjectures concerning these Hecke algebras. One specific example of importance regarding those yet unsolved conjectures is the so-called BMR freeness conjecture. This conjecture is known to be true apart from 16 cases, that are almost all the exceptional groups of rank 2. These exceptional groups of rank 2 fall into three families: the tetrahedral, octahedral and icosahedral family. We prove the validity of the BMR freeness conjecture for the exceptional groups belonging to the first two families, using a case-by-case analysis and we give a nice description of the basis, similar to the classical case of the finite Coxeter groups. We also give a new consequence of this conjecture, by obtaining the classification of irreducible representations of the braid group on 3 strands in dimension at most 5, recovering results of Tuba and Wenzl.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-02T14:23:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "exceptional groups",
      "broué-malle-rouquier conjecture",
      "bmr freeness conjecture",
      "finite coxeter group",
      "hecke algebra"
    ],
    "tags": [
      "dissertation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}