{
  "id": "0909.3394",
  "version": "v4",
  "published": "2009-09-18T13:03:23.000Z",
  "updated": "2010-06-04T07:43:56.000Z",
  "title": "Some Non-Trivial Kazhdan-Lusztig Coefficients of an Affine Weyl Group of Type $\\tilde A_n$",
  "authors": [
    "Leonard Scott",
    "Nanhua Xi"
  ],
  "comment": "19 pages, to appear in SCIENCE CHINA Mathematics",
  "categories": [
    "math.RT",
    "math.CO"
  ],
  "abstract": "In this paper we show that the leading coefficient $\\mu(y,w)$ of some Kazhdan-Lusztig polynomials $P_{y,w}$ with $y,w$ in an affine Weyl group of type $\\tilde A_n $ is $n+2$. This fact has some consequences on the dimension of first extension groups of finite groups of Lie type with irreducible coefficients.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2010-06-04T07:43:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C08"
    ],
    "keywords": [
      "affine weyl group",
      "non-trivial kazhdan-lusztig coefficients",
      "first extension groups",
      "kazhdan-lusztig polynomials",
      "lie type"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1007/s11425-010-4041-4",
      "journal": "Science in China A: Mathematics",
      "year": 2010,
      "month": "Aug",
      "volume": 53,
      "number": 8,
      "pages": 1919
    },
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010ScChA..53.1919S"
    }
  }
}