The symmetry of the partition function of some square ice models

Abstract

We consider the partition function Z(N; x 1 , …, xN, y 1 , …, yN) of the square ice model with domain wall boundary conditions. We give a simple proof that Z is symmetric with respect to all its variables when the global parameter a of the model is set to the special value a = eiπ/3. Our proof does not use any determinant interpretation of Z and can be adapted to other situations (e.g., to some symmetric ice models).