Elliptic Ruijsenaars-Schneider model via the Poisson reduction of the Affine Heisenberg Double

TL;DR

This paper demonstrates how the elliptic Ruijsenaars-Schneider model can be derived from the affine Heisenberg Double using Poisson reduction, highlighting the role of the dynamical r-matrix in the process.

Contribution

It introduces a novel derivation of the elliptic Ruijsenaars-Schneider model from the affine Heisenberg Double via Poisson reduction, emphasizing the emergence of the dynamical r-matrix.

Findings

Elliptic Ruijsenaars-Schneider model obtained from affine Heisenberg Double.

Dynamical r-matrix appears naturally in the construction.

Provides a new geometric perspective on the model's derivation.

Abstract

It is shown that the elliptic Ruijsenaars-Schneider model can be obtained from the affine Heisenberg Double by means of the Poisson reduction procedure. The dynamical $r$-matrix naturally appears in the construction.