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

M. Ciucu and C. Krattenthaler
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M. Ciucu: Indiana University, Department of Mathematics
C. Krattenthaler: Universität Wien, Fakultät für Mathematik

Chapter Chapter 3 in Advances in Combinatorial Mathematics, 2009, pp 39-59 from Springer

Abstract: 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).

Date: 2009
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DOI: 10.1007/978-3-642-03562-3_3

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