The \(A_ n^{(1)}\) face models (Q1117311)

Presented here is the construction of solvable two-dimensional lattice models associated with the affine Lie algebra \(A_ n^{(1)}\) and an arbitrary pair of Young diagrams. The models comprise two kinds of fluctuation variables; one lives on the sites and takes on dominant integral weights of a fixed level, the other lives on edges and assumes the weights of the representations of \(sl(n+1,{\mathbb{C}})\) specified by Young diagrams. The Boltzmann weights are elliptic solutions of the Yang- Baxter equation. Some conjectures on the one point functions are put forth.