From Dynamical to Numerical R-Matrices: A Case Study for the Calogero Models

TL;DR

This paper investigates the possibility of transforming the Lax pair of Calogero models, associated with Lie algebras, from a dynamical R-matrix form to a numerical R-matrix form through gauge transformations.

Contribution

It provides a detailed case study on the gauge transformation process for Calogero models, expanding understanding of their integrable structure.

Findings

Identifies conditions under which gauge transformations yield numerical R-matrices.

Clarifies the relationship between dynamical and numerical R-matrices in Calogero models.

Enhances the theoretical framework for analyzing integrable systems with Lie algebra symmetries.

Abstract

Within the class of integrable Calogero models associated with (semi-)simple Lie algebras and with symmetric pairs of Lie algebras identified in a previous paper, we analyze whether and to what extent it is possible to find a gauge transformation that takes the traditional Lax pair with its dynamical R-matrix to a new Lax pair with a numerical R-matrix.