Factorization dynamics and Coxeter-Toda lattices
solv-int
2009-10-31 v2 Quantum Algebra
Exactly Solvable and Integrable Systems
Abstract
It is shown that the factorization relation on simple Lie groups with standard Poisson Lie structure restricted to Coxeter symplectic leaves gives an integrable dynamical system. This system can be regarded as a discretization of the Toda flow. In case of the integrals of the factorization dynamics are integrals of the relativistic Toda system. A substantial part of the paper is devoted to the study of symplectic leaves in simple complex Lie groups, its Borel subgroups and their doubles.
Keywords
Cite
@article{arxiv.solv-int/9906013,
title = {Factorization dynamics and Coxeter-Toda lattices},
author = {Tim Hoffmann and Johannes Kellendonk and Nadja Kutz and Nicolai Reshetikhin},
journal= {arXiv preprint arXiv:solv-int/9906013},
year = {2009}
}
Comments
33 pages, latex, minor corrections