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Weighted Aztec diamond graphs and the Weyl character formula. (English) Zbl 1053.52025
Electron. J. Comb. 11, No. 1, Research paper R28, 16 p. (2004); printed version J. Comb. 11, No. 1 (2004).
Summary: Special weight labelings on Aztec diamond graphs lead to sum-product identities through a recursive formula of Kou. 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.

##### MSC:
 52C20 Tilings in $$2$$ dimensions (aspects of discrete geometry) 05B45 Combinatorial aspects of tessellation and tiling problems 17B10 Representations of Lie algebras and Lie superalgebras, algebraic theory (weights)
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