Solving the open XXZ spin chain with nondiagonal boundary terms at roots of unity

We consider the open XXZ quantum spin chain with nondiagonal boundary terms.: For bulk anisotropy value eta = ipi/p+1, p = 1, 2,..., we propose an exact (p + 1)-order functional relation for the transfer matrix, which implies Bethe-ansatz-like equations for the corresponding eigenvalues. The key observation is that the fused spin-p+1/ 2 transfer matrix can be expressed in terms of a lower-spin transfer matrix, resulting in the truncation of the fusion hierarchy. (C) 2002 Elsevier Science B.V. All rights reserved.