{
  "id": "1406.7860",
  "version": "v1",
  "published": "2014-06-30T19:17:48.000Z",
  "updated": "2014-06-30T19:17:48.000Z",
  "title": "Peak algebras, paths in the Bruhat graph and Kazhdan-Lusztig polynomials",
  "authors": [
    "Francesco Brenti",
    "Fabrizio Caselli"
  ],
  "comment": "31 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "We give a new characterization of the peak subalgebra of the algebra of quasisymmetric functions and use this to construct a new basis for this subalgebra. As an application of these results we obtain a combinatorial formula for the Kazhdan-Lusztig polynomials which holds in complete generality and is simpler and more explicit than any existing one. We then show that, in a certain sense, this formula cannot be simplified.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-06-30T19:17:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E10"
    ],
    "keywords": [
      "kazhdan-lusztig polynomials",
      "bruhat graph",
      "peak algebras",
      "complete generality",
      "quasisymmetric functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 31,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1406.7860B"
    }
  }
}