Weighted Aztec Diamond Graphs and the Weyl Character Formula

Abstract

Special weight labelings on Aztec diamond graphs lead to sum-product identities through a recursive formula of Kuo. The weight assigned to each perfect matching of the graph is a Laurent monomial, and the identities in these monomials combine to give Weyl's character formula for the representation with highest weight $\rho$ (the half sum of the positive roots) for the classical Lie algebras.