{
  "id": "1203.1640",
  "version": "v4",
  "published": "2012-03-07T21:35:53.000Z",
  "updated": "2013-12-09T21:03:21.000Z",
  "title": "A combinatorial description of the affine Gindikin-Karpelevich formula of type A_n^(1)",
  "authors": [
    "Seok-Jin Kang",
    "Kyu-Hwan Lee",
    "Hansol Ryu",
    "Ben Salisbury"
  ],
  "comment": "20 pages; v2 Correction to the formula of Braverman, Finkelberg, and Kazhdan; v3 Minor correction; v4 Sage examples added",
  "categories": [
    "math.RT",
    "math.CO"
  ],
  "abstract": "The classical Gindikin-Karpelevich formula appears in Langlands' calculation of the constant terms of Eisenstein series on reductive groups and in Macdonald's work on p-adic groups and affine Hecke algebras. The formula has been generalized in the work of Garland to the affine Kac-Moody case, and the affine case has been geometrically constructed in a recent paper of Braverman, Finkelberg, and Kazhdan. On the other hand, there have been efforts to write the formula as a sum over Kashiwara's crystal basis or Lusztig's canonical basis, initiated by Brubaker, Bump, and Friedberg. In this paper, we write the affine Gindikin-Karpelevich formula as a sum over the crystal of generalized Young walls when the underlying Kac-Moody algebra is of affine type A_n^(1). The coefficients of the terms in the sum are determined explicitly by the combinatorial data from Young walls.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2013-12-09T21:03:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "17B37",
      "05E10"
    ],
    "keywords": [
      "affine gindikin-karpelevich formula",
      "combinatorial description",
      "young walls",
      "kashiwaras crystal basis",
      "classical gindikin-karpelevich formula appears"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1203.1640K"
    }
  }
}