On trigonometric intertwining vectors and non-dynamical R-matrix for the Ruijsenaars model

TL;DR

This paper develops a trigonometric version of intertwining vectors and L-operators for the Ruijsenaars model, revealing multiple degenerations and introducing a non-dynamical R-matrix different from standard forms.

Contribution

It introduces a novel trigonometric construction for intertwining vectors and L-operators, including a non-dynamical R-matrix for the Ruijsenaars model, expanding the understanding of degenerations and connections to dynamical R-matrices.

Findings

Constructed several trigonometric degenerations of elliptic intertwining vectors.

Derived a quantum Lax operator for the Ruijsenaars model with a non-dynamical R-matrix.

Identified differences from standard trigonometric R-matrices of type A_n.

Abstract

We elaborate the trigonometric version of intertwining vectors and factorized L-operators. The starting point is the corresponding elliptic construction with Belavin's R-matrix. The naive trigonometric limit is singular and a careful analysis is needed. It is shown that the construction admits several different trigonometric degenerations. As a by-product, a quantum Lax operator for the trigonometric Ruijsenaars model intertwined by a non-dynamical R-matrix is obtained. The latter differs from the standard trigonometric R-matrix of $A_n$ type. A connection with the dynamical R-matrix approach is discussed.