The 6-vertex model and deformations of the Weyl character formula

Abstract

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 to 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.