Scalar Products in Generalized Models with SU(3)-Symmetry

We consider a generalized model with SU(3)-invariant R-matrix, and review the nested Bethe Ansatz for constructing eigenvectors of the transfer matrix. A sum formula for the scalar product between generic Bethe vectors, originally obtained by Reshetikhin, is discussed. This formula depends on a certain partition function Z({λ}, {μ}|{w}, {v}), which we evaluate explicitly. In the limit when the variables {μ} or ${\{v\}\rightarrow \infty}$ , this object reduces to the domain wall partition function of the six-vertex model Z({λ}|{w}). Using this fact, we obtain a new expression for the off-shell scalar product (between a generic Bethe vector and a Bethe eigenvector), in the case when one set of Bethe variables tends to infinity. The expression obtained is a product of determinants, one of which is the Slavnov determinant from SU(2) theory.