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 [11], is discussed. This formula depends on a certain partition function Z(\{ \lambda\},\{ \mu\}|\{ w\},\{ v\}), which we evaluate explicitly. In the limit when the variables \{ \mu\} or \{ v\} approach infinity, this object reduces to the domain wall partition function of the six-vertex model Z(\{ \lambda\}|\{ 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. It extends a result of Caetano [13].
Categories: math-ph hep-th math.MP
