Exact solution of solid-on-solid models for twisted affine Lie algebras A2n(2) and A2n-1(2)

We report new exact solutions of restricted and unrestricted solid-on-solid (SOS) models associated with the twisted affine Lie algebras Xn(2)=A2n(2) and A(2)2n-1. The Boltzmann weights are parametrized by elliptic theta functions and fulfill the Yang-Baxter equation. The trigonometric case of the solutions corresponds to the SOS counterpart of the solvable vertex models arising from the Xn(2) quantum R-matrices. The restricted models (RSOS) are labeled by the level l as well as the rank n. We show that the level-l A(2)2n-1 RSOS model is equivalent to the level-n Cl(1) RSOS model, which is a manifestation of the level-rank duality. One-point functions of the A(2)2n-1 RSOS model are obtained by using the coset pair Cn(1)+A(1)2n-1containsCn(1). We also determine the one-point functions of the Xn(2) vertex models in terms of Xn(2) string functions. (orig.)