The non-dynamical r-matrices of the degenerate Calogero-Moser models
Feher, L. ; Pusztai, B. G.
arXiv, 0005021 / Harvested from arXiv
A complete description of the non-dynamical r-matrices of the degenerate Calogero-Moser models based on $gl_n$ is presented. First the most general momentum independent r-matrices are given for the standard Lax representation of these systems and those r-matrices whose coordinate dependence can be gauged away are selected. Then the constant r-matrices resulting from gauge transformation are determined and are related to well-known r-matrices. In the hyperbolic/trigonometric case a non-dynamical r-matrix equivalent to a real/imaginary multiple of the Cremmer-Gervais classical r-matrix is found. In the rational case the constant r-matrix corresponds to the antisymmetric solution of the classical Yang-Baxter equation associated with the Frobenius subalgebra of $gl_n$ consisting of the matrices with vanishing last row. These claims are consistent with previous results of Hasegawa and others, which imply that Belavin's elliptic r-matrix and its degenerations appear in the Calogero-Moser models. The advantages of our analysis are that it is elementary and also clarifies the extent to which the constant r-matrix is unique in the degenerate cases.
Publié le : 2000-05-17
Classification:  Mathematical Physics,  High Energy Physics - Theory,  Nonlinear Sciences - Exactly Solvable and Integrable Systems
@article{0005021,
     author = {Feher, L. and Pusztai, B. G.},
     title = {The non-dynamical r-matrices of the degenerate Calogero-Moser models},
     journal = {arXiv},
     volume = {2000},
     number = {0},
     year = {2000},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0005021}
}
Feher, L.; Pusztai, B. G. The non-dynamical r-matrices of the degenerate Calogero-Moser models. arXiv, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/0005021/