{
  "id": "0812.1251",
  "version": "v1",
  "published": "2008-12-06T01:55:22.000Z",
  "updated": "2008-12-06T01:55:22.000Z",
  "title": "A factorization theorem for classical group characters, with applications to plane partitions and rhombus tilings",
  "authors": [
    "Mihai Ciucu",
    "Christian Krattenthaler"
  ],
  "comment": "20 pages, AmS-TeX",
  "journal": "in: Advances in Combinatorial Mathematics: Proceedings of the Waterloo Workshop in Computer Algebra 2008, I. Kotsireas, E. Zima (eds.), Springer-Verlag, 2010, pp. 39-60.",
  "categories": [
    "math.CO",
    "math.RT"
  ],
  "abstract": "We prove that a Schur function of rectangular shape $(M^n)$ whose variables are specialized to $x_1,x_1^{-1},...,x_n,x_n^{-1}$ factorizes into a product of two odd orthogonal characters of rectangular shape, one of which is evaluated at $-x_1,...,-x_n$, if $M$ is even, while it factorizes into a product of a symplectic character and an even orthogonal character, both of rectangular shape, if $M$ is odd. It is furthermore shown that the first factorization implies a factorization theorem for rhombus tilings of a hexagon, which has an equivalent formulation in terms of plane partitions. A similar factorization theorem is proven for the sum of two Schur functions of respective rectangular shapes $(M^n)$ and $(M^{n-1})$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-12-06T01:55:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05E15",
      "05A15",
      "05A17",
      "05A19",
      "05B45",
      "11P81",
      "20C15",
      "20G05",
      "52C20"
    ],
    "keywords": [
      "classical group characters",
      "rhombus tilings",
      "plane partitions",
      "schur function",
      "applications"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "AMS-TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0812.1251C"
    }
  }
}