Solvable lattice models related to the vector representation of classical simple Lie algebras

A series of solvable lattice models with face interaction are introduced on the basis of the affine Lie algebraX (1) =A (1) ,B (1) ,C (1) ,D (1) . The local states taken on by the fluctuation variables are the dominant integral weights ofX (1) of a fixed level. Adjacent local states are subject to a condition related to the vector representation ofX n . The Boltzmann weights are parametrized by elliptic theta functions and solve the star-triangle relation.