Truncation of functional relations in the XXZ model

The integrable XXZ model with a special open boundary condition is considered. We study the Sklyanin transfer matrices after the quantum group reduction at roots of unity. In this case, the Sklyanin transfer matrices satisfy a closed system of truncated functional equations. The algebraic reason for the truncation is found. An important role in the proof of the result is played by the Zamolodchikov algebra introduced in the paper.