Generalized T-Q relations and the open XXZ chain

We propose a generalization of the Baxter T-Q relation which involves more than one independent Q(u). We argue that the eigenvalues of the transfer matrix of the open XXZ quantum spin chain are given by such generalized T-Q relations, for the case that at most two of the boundary parameters {\alpha_-, \alpha_+, \beta_-, \beta_+} are nonzero, and the bulk anisotropy parameter has values \eta = i \pi/2, i\pi/4, ...