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).
