{
  "id": "2404.04961",
  "version": "v1",
  "published": "2024-04-07T13:45:27.000Z",
  "updated": "2024-04-07T13:45:27.000Z",
  "title": "0-Hecke Modules, Domino Tableaux, and Type-$B$ Quasisymmetric Functions",
  "authors": [
    "Colin Defant",
    "Dominic Searles"
  ],
  "comment": "25 pages, 3 figures",
  "categories": [
    "math.CO",
    "math.RT"
  ],
  "abstract": "We extend the notion of ascent-compatibility from symmetric groups to all Coxeter groups, thereby providing a type-independent framework for constructing families of modules of $0$-Hecke algebras. We apply this framework in type $B$ to give representation-theoretic interpretations of a number of noteworthy families of type-$B$ quasisymmetric functions. Next, we construct modules of the type-$B$ $0$-Hecke algebra corresponding to type-$B$ analogues of Schur functions and introduce a type-$B$ analogue of Schur $Q$-functions; we prove that these shifted domino functions expand positively in the type-$B$ peak functions. We define a type-$B$ analogue of the $0$-Hecke--Clifford algebra, and we use this to provide representation-theoretic interpretations for both the type-$B$ peak functions and the shifted domino functions. We consider the modules of this algebra induced from type-$B$ $0$-Hecke modules constructed via ascent-compatibility and prove a general formula, in terms of type-$B$ peak functions, for the type-$B$ quasisymmetric characteristics of the restrictions of these modules.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-04-07T13:45:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E05",
      "05E10",
      "20C08"
    ],
    "keywords": [
      "quasisymmetric functions",
      "domino tableaux",
      "peak functions",
      "hecke algebra",
      "representation-theoretic interpretations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}