{
  "id": "2105.14169",
  "version": "v1",
  "published": "2021-05-29T01:17:58.000Z",
  "updated": "2021-05-29T01:17:58.000Z",
  "title": "Weak Bruhat interval modules of the 0-Hecke algebra",
  "authors": [
    "Woo-Seok Jung",
    "Young-Hun Kim",
    "So-Yeon Lee",
    "Young-Tak Oh"
  ],
  "comment": "40 pages",
  "categories": [
    "math.RT",
    "math.CO"
  ],
  "abstract": "To each left weak Bruhat interval $[\\sigma,\\rho]_L$ we assign an $H_n(0)$-module $\\mathsf{B}(\\sigma,\\rho)$, called the weak Bruhat interval module associated to $[\\sigma,\\rho]_L$. The family of weak Bruhat interval modules contains many important $H_n(0)$-modules such as projective indecomposable modules, irreducible modules, and their induced modules. We study embedding problem, induction product, restriction, and (anti-)involution twists of these modules. And, we prove that various $H_n(0)$-modules arising from the context of the quasisymmetric characteristic are decomposed into indecomposable weak Bruhat interval modules.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-05-29T01:17:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C08",
      "05E10",
      "05E05"
    ],
    "keywords": [
      "weak bruhat interval modules contains",
      "left weak bruhat interval",
      "indecomposable weak bruhat interval modules",
      "induction product",
      "study embedding problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}