{
  "id": "0804.3781",
  "version": "v3",
  "published": "2008-04-23T19:00:05.000Z",
  "updated": "2008-12-16T21:52:24.000Z",
  "title": "Hecke group algebras as quotients of affine Hecke algebras at level 0",
  "authors": [
    "Florent Hivert",
    "Anne Schilling",
    "Nicolas M. Thiéry"
  ],
  "comment": "21 pages; 4 figures v2: improved presentation, 23 pages v3: final proofreading, to appear in Journal of Combinatorial Theory Series A",
  "journal": "Journal of Combinatorial Theory, Series A 116 (2009) 844-863",
  "doi": "10.1016/j.jcta.2008.11.010",
  "categories": [
    "math.RT",
    "math.CO"
  ],
  "abstract": "The Hecke group algebra $HW_0$ of a finite Coxeter group $W_0$, as introduced by the first and last author, is obtained from $W_0$ by gluing appropriately its 0-Hecke algebra and its group algebra. In this paper, we give an equivalent alternative construction in the case when $W_0$ is the classical Weyl group associated to an affine Weyl group $W$. Namely, we prove that, for $q$ not a root of unity, $HW_0$ is the natural quotient of the affine Hecke algebra through its level 0 representation. We further show that the level 0 representation is a calibrated principal series representation for a suitable choice of character, so that the quotient factors (non trivially) through the principal central specialization. This explains in particular the similarities between the representation theory of the classical 0-Hecke algebra and that of the affine Hecke algebra at this specialization.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2008-12-16T21:52:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C08",
      "05E15"
    ],
    "keywords": [
      "affine hecke algebra",
      "hecke group algebra",
      "affine weyl group",
      "finite coxeter group",
      "calibrated principal series representation"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "inspire": 800373,
      "adsabs": "2008arXiv0804.3781H"
    }
  }
}