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

TL;DR

This paper characterizes the most general momentum-independent dynamical r-matrices for degenerate Calogero-Moser models based on gl_n, identifying those that can be gauged away and providing explicit solutions in the rational case.

Contribution

It classifies and explicitly constructs the gauge-equivalent non-dynamical r-matrices for these models, expanding understanding of their algebraic structure.

Findings

Explicit non-dynamical r-matrix solution in the rational case

Identification of r-matrices with gauge dependence that can be eliminated

Connection to Frobenius subalgebra of gl_n

Abstract

The most general momentum independent dynamical r-matrices are described for the standard Lax representation of the degenerate Calogero-Moser models based on $gl_n$ 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 $gl_n$ consisting of the matrices with vanishing last row.