Arthemy V. Kiselev (J.Bernoulli Institute, University of Groningen, Netherlands)

The integrals of motion for the 2D Toda chains: their nature and their origin. An open problem.

Abstract:
   We address the problem of invariant definition (in terms of the root systems) and construction of the integrals of motion for the non-periodic 2D Toda chains associated with the root systems of semi-simple complex Lie algebras. We reformulate this problem, which initially emerged for the gauge-invariant Yang-Mills models and their symmetry reductions, in the context of Lie algebroids over the infinite jet spaces and their anchors. The talk is based on the sequence of recent publications arXiv:nlin.SI/0901.4866, nlin.SI/0902.3624, math-ph/0904.1555, and math.DG/1006.4227 (joint with J.W.van de Leur).