{
  "id": "1912.02840",
  "version": "v1",
  "published": "2019-12-05T19:06:57.000Z",
  "updated": "2019-12-05T19:06:57.000Z",
  "title": "Cambrian combinatorics on quiver representations (type A)",
  "authors": [
    "Emily Barnard",
    "Emily Gunawan",
    "Emily Meehan",
    "Ralf Schiffler"
  ],
  "comment": "22 pages, 14 figures. Comments are welcome",
  "categories": [
    "math.RT",
    "math.CO",
    "math.RA"
  ],
  "abstract": "This paper presents a new geometric model of the Auslander-Reiten quiver of a type A quiver. We introduce a new Catalan object which we call a maximal almost rigid representation. We show that its endomorphism algebra is a tilted algebra of type A. We define a partial order on the set of maximal almost rigid representations and use our new geometric model to show that this partial order is a Cambrian lattice.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-12-05T19:06:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E10",
      "16G20",
      "16G70"
    ],
    "keywords": [
      "quiver representations",
      "cambrian combinatorics",
      "geometric model",
      "partial order",
      "rigid representation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}