On the construction and solution of [formula omitted]-symmetric models

Abstract

The U q( gl ′(2,1; C)) symmetric R-matrix, acting on the direct product of a four-dimensional representation of this algebra with itself, constructed by Gould et al., is generalized to the case of two different four-dimensional not necessarily unitary representations and to the case of a product of these with the fundamental one. The latter is used in the algebraic Bethe ansatz solution of some models. Together with the R-matrix acting on the product of the fundamental representation with itself, these fundamental R-matrices form the starting point of an infinite fusion hierarchy of exactly solvable models. A number of these are constructed explicitly. Some Bethe ansatz equations for the eigenvalues of their transfer matrices are derived.