On the symmetry of the partition function of some square ice models

We consider the partition function Z(N;x_1,...,x_N,y_1,...,y_N) of the square ice model with domain wall boundary. We give a simple proof of the symmetry of Z with respect to all its variables when the global parameter a of the model is set to the special value a=exp(iπ/3). Our proof does not use any determinantal interpretation of Z and can be adapted to other situations (for examples to some symmetric ice models).

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