{
  "id": "2303.09251",
  "version": "v1",
  "published": "2023-03-16T12:02:02.000Z",
  "updated": "2023-03-16T12:02:02.000Z",
  "title": "Parabolic recursions for Kazhdan-Lusztig polynomials and the hypercube decomposition",
  "authors": [
    "Maxim Gurevich",
    "Chuijia Wang"
  ],
  "comment": "23 pages, comments welcome",
  "categories": [
    "math.RT",
    "math.CO"
  ],
  "abstract": "We employ general parabolic recursion methods to demonstrate the recently devised hypercube formula for Kazhdan-Lusztig polynomials of $S_n$, and establish its generalization to the full setting of a finite Coxeter system through algebraic proof. We introduce procedures for positive decompositions of $q$-derived Kazhdan-Lusztig polynomials within this setting, that utilize classical Hecke algebra positivity phenomena of Dyer-Lehrer and Grojnowski-Haiman. This leads to a distinct algorithmic approach to the subject, based on induction from a parabolic subgroup. We propose suitable weak variants of the combinatorial invariance conjecture and verify their validity for permutation groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-16T12:02:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "kazhdan-lusztig polynomials",
      "hypercube decomposition",
      "employ general parabolic recursion methods",
      "classical hecke algebra positivity phenomena"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}