dorsal/arxiv
View SchemaFactorization dynamics and Coxeter-Toda lattices
| Authors | Tim Hoffmann, Johannes Kellendonk, Nadja Kutz, Nicolai Reshetikhin |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9906013 |
| URL | https://arxiv.org/abs/solv-int/9906013 |
| DOI | 10.1007/s002200000212 |
| Journal | Comm. Math. Phys. 212, Issue 2, 297-321 (2000) |
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 $SL_n$ 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.
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"abstract": "It is shown that the factorization relation on simple Lie groups with\nstandard Poisson Lie structure restricted to Coxeter symplectic leaves gives an\nintegrable dynamical system. This system can be regarded as a discretization of\nthe Toda flow. In case of $SL_n$ the integrals of the factorization dynamics\nare integrals of the relativistic Toda system. A substantial part of the paper\nis devoted to the study of symplectic leaves in simple complex Lie groups, its\nBorel subgroups and their doubles.",
"arxiv_id": "solv-int/9906013",
"authors": [
"Tim Hoffmann",
"Johannes Kellendonk",
"Nadja Kutz",
"Nicolai Reshetikhin"
],
"categories": [
"solv-int",
"math.QA",
"nlin.SI"
],
"doi": "10.1007/s002200000212",
"journal_ref": "Comm. Math. Phys. 212, Issue 2, 297-321 (2000)",
"title": "Factorization dynamics and Coxeter-Toda lattices",
"url": "https://arxiv.org/abs/solv-int/9906013"
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