{
  "id": "math/0507610",
  "version": "v2",
  "published": "2005-07-29T15:26:22.000Z",
  "updated": "2006-04-08T12:37:32.000Z",
  "title": "The $\\hat W$-orbit of $ρ$, Kostant's formula for powers of the Euler product and affine Weyl groups as permutations of Z",
  "authors": [
    "Paola Cellini",
    "Pierluigi Moseneder Frajria",
    "Paolo Papi"
  ],
  "comment": "Latex, 27 pages, minor corrections, to appear in Journal of Pure and Applied Algebra",
  "journal": "J. Pure Appl. Algebra 208 (2007), no. 3, 1103--1119.",
  "categories": [
    "math.RT",
    "math.CO"
  ],
  "abstract": "Let an affine Weyl group $\\hat W$ act as a group of affine transformations on a real vector space V. We analyze the $\\hat W$-orbit of a regular element in V and deduce applications to Kostant's formula for powers of the Euler product and to the representations of $\\hat W$ as permutations of the integers.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2006-04-08T12:37:32.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "affine weyl group",
      "euler product",
      "kostants formula",
      "permutations",
      "real vector space"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "LaTeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......7610C"
    }
  }
}