Schur Polynomials and the Yang-Baxter equation

TL;DR

This paper explores the connection between Schur polynomials and the Yang-Baxter equation within the six-vertex model, revealing a parametrized Yang-Baxter equation with a nonabelian group and deriving deformations of Weyl character formulas.

Contribution

It introduces a parametrized Yang-Baxter equation with a nonabelian parameter group in the six-vertex model and rederives deformations of Weyl character formulas.

Findings

Identifies a nonabelian parameter group GL(2)xGL(1) in the Yang-Baxter equation.

Reproduces deformations of Weyl character formulas by Tokuyama and Hamel-King.

Connects integrable models with algebraic deformations of classical formulas.

Abstract

We show that within the six-vertex model there is a parametrized Yang-Baxter equation with nonabelian parameter group GL(2)xGL(1) at the center of the disordered regime. As an application we rederive deformations of the Weyl character formule of Tokuyama and of Hamel and King.