{
  "id": "math/0608288",
  "version": "v2",
  "published": "2006-08-11T17:44:55.000Z",
  "updated": "2007-08-31T18:16:42.000Z",
  "title": "The Combinatorics of Quiver Representations",
  "authors": [
    "Harm Derksen",
    "Jerzy Weyman"
  ],
  "comment": "63 pages",
  "categories": [
    "math.RT",
    "math.AC",
    "math.AG",
    "math.CO"
  ],
  "abstract": "We give a description of faces of all codimensions for the cones of weights of rings of semi-invariants of quivers. For a triple flag quiver and faces of codimension 1 this reduces to the result of Knutson-Tao-Woodward on the facets of the Klyachko cone. We give new applications to Littlewood-Richardson coefficients, including a product formula for LR-coefficients corresponding to triples of partitions lying on a wall of the Klyachko cone. We systematically review and develop the necessary methods (exceptional and Schur sequences, orthogonal categories, semi-stable decompositions, GIT quotients for quivers). In the Appendix we include a version of Belkale's geometric proof of Fulton's conjecture that works for arbitrary quivers.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-08-31T18:16:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G20",
      "14L24",
      "13A50",
      "05E15"
    ],
    "keywords": [
      "quiver representations",
      "combinatorics",
      "klyachko cone",
      "belkales geometric proof",
      "triple flag quiver"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 63,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......8288D"
    }
  }
}