{
  "id": "0803.0842",
  "version": "v1",
  "published": "2008-03-06T11:59:43.000Z",
  "updated": "2008-03-06T11:59:43.000Z",
  "title": "Leading coefficients and cellular bases of Hecke algebras",
  "authors": [
    "Meinolf Geck"
  ],
  "comment": "22 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "Let $\\bH$ be the generic Iwahori--Hecke algebra associated with a finite Coxeter group $W$. Recently, we have shown that $\\bH$ admits a natural cellular basis in the sense of Graham--Lehrer, provided that $W$ is a Weyl group and all parameters of $\\bH$ are equal. The construction involves some data arising from the Kazhdan--Lusztig basis $\\{\\bC_w\\}$ of $\\bH$ and Lusztig's asymptotic ring $\\bJ$. This article attemps to study $\\bJ$ and its representation theory from a new point of view. We show that $\\bJ$ can be obtained in an entirely different fashion from the generic representations of $\\bH$, without any reference to $\\{\\bC_w\\}$. Then we can extend the construction of the cellular basis to the case where $W$ is not crystallographic. Furthermore, if $\\bH$ is a multi-parameter algebra, we will see that there always exists at least one cellular structure on $\\bH$. Finally, one may also hope that the new construction of $\\bJ$ can be extended to Hecke algebras associated to complex reflection groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-03-06T11:59:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C08"
    ],
    "keywords": [
      "hecke algebras",
      "cellular bases",
      "leading coefficients",
      "finite coxeter group",
      "natural cellular basis"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0803.0842G"
    }
  }
}