  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(i\pi/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).
