This material has been published 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, the only definitive repository of the content that has been certified and accepted after peer review. Copyright and all rights therein are retained by Springer-Verlag. This material may not be copied or reposted without explicit permission.

Mihai Ciucu and Christian Krattenthaler

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

(19 pages)

Abstract. We prove that a Schur function of rectangular shape (Mn) whose variables are specialized to x1,x1-1,...,xn,xn-1 factorizes into a product of two odd orthogonal characters of rectangular shape, one of which is evaluated at -x1,...,-xn, 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 (Mn) and (Mn-1).

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