Remarks on $A^{(1)}_n$ face weights

Understand

Elementary proofs are presented for the factorization of the elliptic Boltzmann weights of the $A^{(1)}_n$ face model, and for the sum-to-1 property in the trigonometric limit, at a special point of the spectral parameter.

• They generalize recent results obtained in the context of the corresponding trigonometric vertex model.