Title: Schur Polynomials and The Yang-Baxter Equation

Abstract: Schur polynomials are symmetric polynomials describing the characters of irreducible representations of GL(n,C). They are expressed by the Weyl character formula. Deformations of the Weyl character formula giving interesting representations of Schur polynomials were found by Tokuyama and by Hamel and King. The Hamel-King representation shows that it is possible to assign Boltzmann weights in the six-vertex model for two dimensional ice which describes the Schur polynomial (times a deformation of the Weyl denominator) as the partition function of a statistical mechanical system. Now Baxter gave a method of evaluating such partition functions based on the star-triangle identity or Yang-Baxter equation, which is the starting point of the theory of quantum groups. Brubaker, Bump and Friedberg investigated the implications of Baxter's method in this context, obtaining new proofs of the results of Tokuyama and Hamel-King. Moreover, a fascinating algebraic picture emerges, with two distinct types of ice related by four types of R-matrices satisfying exactly the relations needed to define a Drinfeld double Hopf algebra.

URL: http://sporadic.stanford.edu/bump/hkice.pdf