On the separation of variables for the modular XXZ magnet and the lattice Sinh-Gordon models
Résumé
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 $L^2(\mathbb {R}^N)$ . 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.