{
  "id": "2109.09803",
  "version": "v1",
  "published": "2021-09-20T19:22:50.000Z",
  "updated": "2021-09-20T19:22:50.000Z",
  "title": "Kazhdan--Lusztig cells of $\\mathbf{a}$-value 2 in $\\mathbf{a}(2)$-finite Coxeter systems",
  "authors": [
    "R. M. Green",
    "Tianyuan Xu"
  ],
  "comment": "44 pages",
  "categories": [
    "math.CO",
    "math.RT"
  ],
  "abstract": "A Coxeter group is said to be \\emph{$\\mathbf{a}(2)$-finite} if it has finitely many elements of $\\mathbf{a}$-value 2 in the sense of Lusztig. In this paper, we give explicit combinatorial descriptions of the left, right, and two-sided Kazhdan--Lusztig cells of $\\mathbf{a}$-value 2 in an irreducible $\\mathbf{a}(2)$-finite Coxeter group. In particular, we introduce elements we call \\emph{stubs} to parameterize the one-sided cells and we characterize the one-sided cells via both star operations and weak Bruhat orders. We also compute the cardinalities of all the one-sided and two-sided cells.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-09-20T19:22:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20F55",
      "20C08"
    ],
    "keywords": [
      "finite coxeter systems",
      "explicit combinatorial descriptions",
      "finite coxeter group",
      "one-sided cells",
      "weak bruhat orders"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 44,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}