{
  "id": "1106.0535",
  "version": "v2",
  "published": "2011-06-02T23:22:34.000Z",
  "updated": "2012-01-20T16:07:02.000Z",
  "title": "A combinatorial description of the Gindikin-Karpelevich formula in type A",
  "authors": [
    "Kyu-Hwan Lee",
    "Ben Salisbury"
  ],
  "comment": "17 pages. Edited using comments from referees",
  "journal": "J. Combin. Theory Ser. A. 119 (2012), 1081-1094",
  "doi": "10.1016/j.jcta.2012.01.011",
  "categories": [
    "math.CO",
    "math.RT"
  ],
  "abstract": "A combinatorial description of the crystal $\\mathcal{B}(\\infty)$ for finite-dimensional simple Lie algebras in terms of Young tableaux was developed by J. Hong and H. Lee. Using this description, we obtain a combinatorial rule for expressing the Gindikin-Karpelevich formula as a sum over $\\mathcal{B}(\\infty)$ when the underlying Lie algebra is of type A. We also interpret our description in terms of MV polytopes and irreducible components of quiver varieties.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-01-20T16:07:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "gindikin-karpelevich formula",
      "combinatorial description",
      "finite-dimensional simple lie algebras",
      "young tableaux",
      "combinatorial rule"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1106.0535L"
    }
  }
}