The finite XXZ model with boundaries is considered. We use the matrix produ
ct ansatz (MPA), which was originally developed in the studies on the asymm
etric simple exclusion process and the quantum antiferromagnetic spin chain
. The MPA demonstrates that the eigenstate of the Hamiltonian is constructe
d by the Zamolodchikov-Faddeev algebra (ZF-algebra) and the boundary states
. We adopt the type I vertex operator of U-q((s) over cap l(2)) as the ZF-a
lgebra and realize the boundary states in the bosonic U-q((s) over cap l(2)
) form. The correlation functions are given by the product of the vertex op
erators and the bosonic boundary states. We express them in the integration
forms. (C) 2000 Elsevier Science Ltd. All rights reserved.