Poisson-Lie generalization of the Kazhdan-Kostant-Sternberg reduction
Mathematical Physics
2009-11-13 v2 math.MP
Symplectic Geometry
Exactly Solvable and Integrable Systems
Abstract
The trigonometric Ruijsenaars-Schneider model is derived by symplectic reduction of Poisson-Lie symmetric free motion on the group U(n). The commuting flows of the model are effortlessly obtained by reducing canonical free flows on the Heisenberg double of U(n). The free flows are associated with a very simple Lax matrix, which is shown to yield the Ruijsenaars-Schneider Lax matrix upon reduction.
Keywords
Cite
@article{arxiv.0809.1509,
title = {Poisson-Lie generalization of the Kazhdan-Kostant-Sternberg reduction},
author = {L. Feher and C. Klimcik},
journal= {arXiv preprint arXiv:0809.1509},
year = {2009}
}
Comments
13 pages, LaTeX, minor modifications and references added in v2