Factorization dynamics and Coxeter-Toda lattices

Tim Hoffmann, Johannes Kellendonk, Nadja Kutz, Nicolai Reshetikhin

Research output: Contribution to journalArticlepeer-review

34 Scopus citations

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 SLn the integrals of the factorization dynamics are integrals of the relativistic Toda system. A substantial part of the paper is devoted to the description of symplectic leaves in simple complex Lie groups, its Borel subgroups and their doubles.

Original languageEnglish
Pages (from-to)297-321
Number of pages25
JournalCommunications in Mathematical Physics
Volume212
Issue number2
DOIs
StatePublished - 2000
Externally publishedYes

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