Factorization dynamics and Coxeter-Toda lattices

Citation
T. Hoffmann et al., Factorization dynamics and Coxeter-Toda lattices, COMM MATH P, 212(2), 2000, pp. 297-321
Citations number
36
Categorie Soggetti
Physics
Journal title
COMMUNICATIONS IN MATHEMATICAL PHYSICS
ISSN journal
00103616 → ACNP
Volume
212
Issue
2
Year of publication
2000
Pages
297 - 321
Database
ISI
SICI code
0010-3616(200007)212:2<297:FDACL>2.0.ZU;2-F
Abstract
It is shown that the factorization relation on simple Lie groups with stand ard Poisson Lie structure restricted to Coxeter symplectic leaves gives an integrable dynamical system. This system can be regarded as a discretizatio n of the Toda flow. In case of SLn the integrals of the factorization dynam ics are integrals of the relativistic Toda system. A substantial part of th e paper is devoted to the description of symplectic leaves in simple comple x Lie groups, its Borel subgroups and their doubles.