{
  "id": "2308.01585",
  "version": "v1",
  "published": "2023-08-03T07:41:47.000Z",
  "updated": "2023-08-03T07:41:47.000Z",
  "title": "A footnote to a paper of Deodhar",
  "authors": [
    "Davide Franco"
  ],
  "comment": "12 pages",
  "categories": [
    "math.AG",
    "math.RT"
  ],
  "abstract": "Let $X\\subseteq G\\slash B$ be a Schubert variety in a flag manifold and let $\\pi: \\tilde X \\rightarrow X$ be a Bott-Samelson resolution of $X$. In this paper we prove an effective version of the decomposition theorem for the derived pushforward $R \\pi_{*} \\mathbb{Q}_{\\tilde{X}}$. As a by-product, we obtain recursive procedure to extract Kazhdan-Lusztig polynomials from the polynomials introduced by V. Deodhar in \\cite{Deo}, which does not require prior knowledge of a minimal set. We also observe that any family of equivariant resolutions of Schubert varieties allows to define a new basis in the Hecke algebra and we show a way to compute the transition matrix, from the Kazhdan-Lusztig basis to the new one.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-08-03T07:41:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14B05",
      "14M15",
      "14E15",
      "14F45",
      "32S20",
      "32S60",
      "58K15"
    ],
    "keywords": [
      "schubert variety",
      "extract kazhdan-lusztig polynomials",
      "flag manifold",
      "transition matrix",
      "hecke algebra"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}