{
  "id": "2311.10068",
  "version": "v1",
  "published": "2023-11-16T18:08:45.000Z",
  "updated": "2023-11-16T18:08:45.000Z",
  "title": "Weak Bruhat interval modules of finite-type $0$-Hecke algebras and projective covers",
  "authors": [
    "Joshua Bardwell",
    "Dominic Searles"
  ],
  "comment": "19 pages, 6 figures",
  "categories": [
    "math.RT",
    "math.CO"
  ],
  "abstract": "We extend the recently-introduced weak Bruhat interval modules of the type A $0$-Hecke algebra to all finite Coxeter types. We determine, in a type-independent manner, structural properties for certain general families of these modules, with a primary focus on projective covers and injective hulls. We apply this approach to recover a number of results on type A $0$-Hecke modules in a uniform way, and obtain some additional results on recently-introduced families of type A $0$-Hecke modules.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-11-16T18:08:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E10",
      "20C08",
      "05E05"
    ],
    "keywords": [
      "hecke algebra",
      "projective covers",
      "finite-type",
      "recently-introduced weak bruhat interval modules",
      "hecke modules"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}