Factorization dynamics and Coxeter-Toda lattices

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...

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Bibliographic Details
Published in:arXiv.org 1999-10
Main Authors: Hoffmann, Tim, Kellendonk, Johannes, Kutz, Nadja, Reshetikhin, Nicolai
Format: Article
Language:English
Subjects:
Factorization
Integrals
Lattices
Lie groups
Subgroups
Online Access:Get full text
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.9906013