Baxter operators in Ruijsenaars hyperbolic system IV. Coupling constant reflection symmetry

TL;DR

This paper introduces a new family of Baxter operators in the Ruijsenaars hyperbolic system, demonstrating their commutativity, symmetry properties, and connections to other difference operators, advancing understanding of integrable systems.

Contribution

It presents a novel family of Baxter operators, proves their commutativity, and explores their role in coupling constant symmetry and relations to Noumi-Sano difference operators.

Findings

New Baxter operators commute with existing families.

Coupling constant symmetry of the wave function is verified.

Connections established between Baxter operators and Noumi-Sano difference operators.

Abstract

We introduce and study a new family of commuting Baxter operators in the Ruijsenaars hyperbolic system, different from that considered by us earlier. Using a degeneration of Rains integral identity we verify the commutativity between the two families of Baxter operators and explore this fact for the proof of the coupling constant symmetry of the wave function. We also establish a connection between new Baxter operators and Noumi-Sano difference operators.