On the Separation of Variables for the Modular XXZ Magnet and the Lattice Sinh-Gordon Models

Abstract

We construct the generalised eigenfunctions of the entries of the monodromy matrix of the N-site modular XXZ magnet and show, in each case, that these form a complete orthogonal system in L2(RN). In particular, we develop a new and simple technique, allowing one to prove the completeness of such systems. As a corollary of our analysis, we prove the Bytsko-Teschner conjecture relative to the structure of the spectrum of the B(lambda)-operator for the odd length lattice Sinh-Gordon model.