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_n⁽¹⁾=A_n⁽¹⁾,B_n⁽¹⁾,C_n⁽¹⁾,D_n⁽¹⁾. The local states taken on by the fluctuation variables are the dominant integral weights ofX_n⁽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.