Weighted Aztec Diamond Graphs and the Weyl Character Formula

Georgia Benkart, Oliver Eng


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.

Full Text: PDF