{
  "id": "math/0511380",
  "version": "v3",
  "published": "2005-11-15T13:41:03.000Z",
  "updated": "2006-07-14T20:20:53.000Z",
  "title": "BGP-reflection functors and cluster combinatorics",
  "authors": [
    "Bin Zhu"
  ],
  "comment": "version 3",
  "categories": [
    "math.RT",
    "math.CO"
  ],
  "abstract": "We define Bernstein-Gelfand-Ponomarev reflection functors in the cluster categories of hereditary algebras. They are triangle equivalences which provide a natural quiver realization of the \"truncated simple reflections\" on the set of almost positive roots $\\Phi_{\\ge -1}$ associated to a finite dimensional semisimple Lie algebra. Combining with the tilting theory in cluster categories developed in [4], we give a unified interpretation via quiver representations for the generalized associahedra associated to the root systems of all Dynkin types (a simply-laced or non-simply-laced). This confirms the conjecture 9.1 in [4] in all Dynkin types.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2006-07-14T20:20:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G20",
      "16G70"
    ],
    "keywords": [
      "cluster combinatorics",
      "bgp-reflection functors",
      "finite dimensional semisimple lie algebra",
      "define bernstein-gelfand-ponomarev reflection functors",
      "dynkin types"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....11380Z"
    }
  }
}