%0 Journal Article
%T Factorization dynamics and Coxeter-Toda lattices
%A Tim Hoffmann
%A Johannes Kellendonk
%A Nadja Kutz
%A Nicolai Reshetikhin
%J Physics
%D 1999
%I arXiv
%R 10.1007/s002200000212
%X 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 $SL_n$ 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.
%U http://arxiv.org/abs/solv-int/9906013v2