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 {α_-, α₊, β_-, β₊} are nonzero, and the bulk anisotropy parameter has values η ≤ iπ/2, iπ/4, ....