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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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