Geodesic
The six-vertex model and deformations of the Weyl character formula
Journal of Algebraic Combinatorics, Tome 42 (2015) no. 4, pp. 917-958.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We use statistical mechanics -- variants of the six-vertex model in the plane studied by means of the Yang-Baxter equation -- to give new deformations of Weyl's character formula for classical groups of Cartan type $B$, $C$, and $D$, and a character formula of Proctor for type $BC$. In each case, the corresponding Boltzmann weights are associated with the free fermion point of the six-vertex model. These deformations add to the earlier known examples in types $A$ and $C$ by Tokuyama and Hamel-King, respectively. A special case for classical types recovers deformations of the Weyl denominator formula due to Okada.
Classification : 82B20, 05E10, 05A19, 05C10, 05C90, 20G45, 20G05
Keywords: statistical mechanics, Weyl character formula, Weyl denominator formula, Yang-Baxter equation 
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Brubaker, Ben; Schultz, Andrew. The six-vertex model and deformations of the Weyl character formula. Journal of Algebraic Combinatorics, Tome 42 (2015) no. 4, pp. 917-958. http://geodesic.mathdoc.fr/item/JAC_2015__42_4_a9/