Poisson involutions, spin Calogero-Moser systems associated with symmetric Lie subalgebras and the symmetric space spin Ruijsenaars-Schneider models
Li, Luen-Chau
arXiv, 0506025 / Harvested from arXiv
Text on arXiv
We develop a general scheme to construct integrable systems starting from realizations in symmetric coboundary dynamical Lie algebroids and symmetric coboundary Poisson groupoids. The method is based on the successive use of Dirac reduction and Poisson reduction. Then we show that certain spin Calogero-Moser systems associated with symmetric Lie subalgebras can be studied in this fashion. We also consider some spin-generalized Ruisjenaars- Schneider equations which correspond to the $N$-soliton solutions of $A^{(1)}_n$ affine Toda field theory. In this case, we show how the equations are obtained from the Dirac reduction of some Hamiltonian system on a symmetric coboundary dynamical Poisson groupoid.
Publié le : 2005-06-10
Classification:  Mathematical Physics,  Mathematics - Symplectic Geometry 
@article{0506025,
     author = {Li, Luen-Chau},
     title = {Poisson involutions, spin Calogero-Moser systems associated with
  symmetric Lie subalgebras and the symmetric space spin Ruijsenaars-Schneider
  models},
     journal = {arXiv},
     volume = {2005},
     number = {0},
     year = {2005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0506025}
}

Li, Luen-Chau. Poisson involutions, spin Calogero-Moser systems associated with
  symmetric Lie subalgebras and the symmetric space spin Ruijsenaars-Schneider
  models. arXiv, Tome 2005 (2005) no. 0, . http://gdmltest.u-ga.fr/item/0506025/