{
  "id": "1704.07454",
  "version": "v1",
  "published": "2017-04-24T20:30:00.000Z",
  "updated": "2017-04-24T20:30:00.000Z",
  "title": "Dimer models on cylinders over Dynkin diagrams and cluster algebras",
  "authors": [
    "Maitreyee C. Kulkarni"
  ],
  "categories": [
    "math.RT",
    "math.CO",
    "math.RA"
  ],
  "abstract": "In this paper, we describe a general setting for dimer models on cylinders over Dynkin diagrams which in type A reduces to the well studied case of dimer models on a disc. We prove that all Berenstein--Fomin--Zelevinsky quivers for Schubert cells in a symmetric Kac--Moody algebra give rise to dimer models on the cylinder over the corresponding Dynkin diagram. We also give an independent proof of a result of Buan, Iyama, Reiten and Smith that the corresponding superpotentials are rigid using the dimer model structure of the quivers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-04-24T20:30:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "cluster algebras",
      "symmetric kac-moody algebra",
      "dimer model structure",
      "schubert cells",
      "independent proof"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}