Weighted Aztec Diamond Graphs and the Weyl Character Formula

Georgia Benkart, Oliver Eng

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.


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