{
  "id": "math/0202252",
  "version": "v5",
  "published": "2002-02-24T18:49:56.000Z",
  "updated": "2003-09-30T16:13:06.000Z",
  "title": "Lower bounds for Kazhdan-Lusztig polynomials from patterns",
  "authors": [
    "Sara Billey",
    "Tom Braden"
  ],
  "comment": "14 pages; updated references. Final version; will appear in Transformation Groups vol.8, no. 4",
  "categories": [
    "math.RT",
    "math.AG",
    "math.CO"
  ],
  "abstract": "We give a lower bound for the value at q=1 of a Kazhdan-Lustig polynomial in a Weyl group W in terms of \"patterns''. This is expressed by a \"pattern map\" from W to W' for any parabloic subgroup W'. This notion generalizes the concept of patterns and pattern avoidance for permutations to all Weyl groups. The main tool of the proof is a \"hyperbolic localization\" on intersection cohomology; see the related paper http://front.math.ucdavis.edu/math.AG/0202251",
  "revisions": [
    {
      "version": "v5",
      "updated": "2003-09-30T16:13:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14M15",
      "20F55"
    ],
    "keywords": [
      "lower bound",
      "kazhdan-lusztig polynomials",
      "weyl group",
      "notion generalizes",
      "intersection cohomology"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......2252B"
    }
  }
}