On the classical R-matrix of the degenerate Calogero-Moser models

Abstract

The most general momentum independent dynamical r-matrices are described for the standard Lax representation of the degenerate Calogero-Moser models based on $g{l}_n$ and those r-matrices whose dynamical dependence can be gauged away are selected. In the rational case, a non-dynamical r-matrix resulting from gauge transformation is given explicitly as an antisymmetric solution of the classical Yang-Baxter equation that belongs to the Frobenius subalgebra of $g{l}_n$ consisting of the matrices with vanishing last row.

Talk by L. F. at the 8-th Colloquium on Quantum Groups and Integrable Systems, Prague, June 1999; 7 pages, LaTeX; with new references added

References in corpus (3)

• Calogero-Moser Lax Pairs with Spectral Parameter for General Lie Algebras
• Calogero-Moser Models: A New Formulation
• On trigonometric intertwining vectors and non-dynamical R-matrix for the Ruijsenaars model

Cited by in corpus (4)

• Rational Top and its Classical R-matrix
• The non-dynamical r-matrices of the degenerate Calogero-Moser models
• From Dynamical to Numerical R-Matrices: A Case Study for the Calogero Models
• Totally classical Calogero model