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.
Bibliographical noteFunding Information:
This work was partially supported by NSF Grant DMS-1258675.
© 2015, Springer Science+Business Media New York.
- Statistical mechanics
- Weyl character formula
- Yang–Baxter equation