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A factorization theorem for classical group characters, with applications to plane partitions and rhombus tilings

  • M. Ciucu
  • C. Krattenthaler
Conference paper

Abstract

We prove that a Schur function of rectangular shape (M n ) whose variables are specialized to \(x_{1},x_{1}^{-1},\dots,x_{n},x_{n}^{-1}\) 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).

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • M. Ciucu
    • 1
  • C. Krattenthaler
    • 2
  1. 1.Department of MathematicsIndiana UniversityBloomingtonUSA
  2. 2.Fakultät für MathematikUniversität WienViennaAustria

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