{
  "id": "0805.3463",
  "version": "v2",
  "published": "2008-05-22T13:48:30.000Z",
  "updated": "2010-03-25T07:45:48.000Z",
  "title": "Leading coefficients of the Kazhdan-Lusztig polynomials for an Affine Weyl group of type $\\widetilde{B_2}$",
  "authors": [
    "Liping Wang"
  ],
  "comment": "31 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper we compute the leading coefficients $\\mu (u,w)$ of the Kazhdan--Lusztig polynomials $P_{u,w}$ for an affine Weyl group of type $\\tilde{B}_2$. By using the \\textbf{a}-function of a Coxeter group defined by Lusztig (see [L1, \\S2]), we compute most $\\mu (u,w)$ explicitly. With part of these values $\\mu (u,w)$, we show that a conjecture of Lusztig on distinguished involutions is true for an affine Weyl group of type $\\tilde{B}_2$. We also show that the conjectural formula in [L3, (12)] needs a modification.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2010-03-25T07:45:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E15",
      "20F55"
    ],
    "keywords": [
      "affine weyl group",
      "kazhdan-lusztig polynomials",
      "leading coefficients",
      "conjectural formula",
      "coxeter group"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0805.3463W"
    }
  }
}