Weighted Aztec diamond graphs and the Weyl character formula
The electronic journal of combinatorics, Tome 11 (2004) no. 1
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.
@article{10_37236_1781,
author = {Georgia Benkart and Oliver Eng},
title = {Weighted {Aztec} diamond graphs and the {Weyl} character formula},
journal = {The electronic journal of combinatorics},
year = {2004},
volume = {11},
number = {1},
doi = {10.37236/1781},
zbl = {1053.52025},
url = {http://geodesic.mathdoc.fr/articles/10.37236/1781/}
}
Georgia Benkart; Oliver Eng. Weighted Aztec diamond graphs and the Weyl character formula. The electronic journal of combinatorics, Tome 11 (2004) no. 1. doi: 10.37236/1781
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