{
  "id": "1803.04044",
  "version": "v1",
  "published": "2018-03-11T21:24:00.000Z",
  "updated": "2018-03-11T21:24:00.000Z",
  "title": "Coxeter groups and quiver representations",
  "authors": [
    "Hugh Thomas"
  ],
  "comment": "13 pages",
  "categories": [
    "math.RT",
    "math.CO"
  ],
  "abstract": "In this expository note, I showcase the relevance of Coxeter groups to quiver representations. I discuss (1) real and imaginary roots, (2) reflection functors, and (3) torsion free classes and c-sortable elements. The first two topics are classical, while the third is a more recent development. I show that torsion free classes in rep Q containing finitely many indecomposables correspond bijectively to c-sortable elements in the corresponding Weyl group. This was first established in Dynkin type by Ingalls and Thomas; it was shown in general by Amiot, Iyama, Reiten, and Todorov. The proof in this note is elementary, essentially following the argument of Ingalls and Thomas, but without the assumption that Q is Dynkin.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-03-11T21:24:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quiver representations",
      "coxeter groups",
      "torsion free classes",
      "c-sortable elements",
      "expository note"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}