On Certain Quantization Aspects of (Generalized) Toda Systems

Abstract

Ordinary and gl(n,R) generalized Toda systems as well as a related hierarchy are probed with respect to certain quantization characteristics. "Quantum" canonical and Poisson transformations are used to study quantizations of transformed Toda systems. With a Lax pair setting, a hierarchy of related systems are shown and their quantizations discussed. Finally, comments are added about quantum aspects of gl(n,R) generalized Toda systems with the approaches of deformation quantization or quantum groups in mind.