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We prove that a Schur function of rectangular shape (M  n ) whose variables are specialized to   x1,x1-</font>1,...,xn,xn-</font>1x_{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).

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