Functional Analysis and Applications Seminar 

05/03/2004, 15:00 — 16:00 — Room P3.10, Mathematics Building
Michael A. Semenov-Tian-Shansky, Université de Bourgogne, Dijon, France

Q-Deformed Quantum Toda Lattice: Modular Duality, Separation of Variables, and Baxter Equations

Quantum Toda lattice provides a link between representation theory of semisimple Lie groups and quantum inverse scattering method; its q-deformed version is particularly interesting, since it gives a guide to the representation theory of non-compact quantum groups. This theory is still not fully understood; the study of the q-deformed Toda lattice reveals interesting new phenomena in representation theory : modular duality, first discovered by Faddeev a few years ago (the emergence of a "second" quantum group which is acting in the same representation space and centralizes the action of the first one), and points to the importance of a special class of meromorphic functions (Barnes double sine functions and their relatives). The spectral problem for the q-deformed Toda lattice is inductively reduced to a system of finite difference functional equations (Baxter equations).