{
  "id": "2107.00084",
  "version": "v1",
  "published": "2021-06-30T20:22:10.000Z",
  "updated": "2021-06-30T20:22:10.000Z",
  "title": "An extension of a theorem and errata for \"A Class of Representations of Hecke Algebras\"",
  "authors": [
    "Dean Alvis"
  ],
  "comment": "4 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "By Theorem~1.12 of the paper \"A Class of Representations of Hecke Algebras\", if $W$ is a Coxeter group whose proper parabolic subgroups are finite, and if the module of a finite $W$-digraph $\\Gamma$ is isomorphic to the module of a $W$-graph, then $\\Gamma$ must be acyclic. Here we extend this result to Coxeter groups with finite dihedral parabolic subgroups and $W$-graphs with arbitrary scalar edge labels. Also, errata for the paper are listed in the last section.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-30T20:22:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20C08"
    ],
    "keywords": [
      "hecke algebras",
      "representations",
      "coxeter group",
      "arbitrary scalar edge labels",
      "finite dihedral parabolic subgroups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}