Baxter operators in Ruijsenaars hyperbolic system I. Commutativity of Q-operators

TL;DR

This paper introduces Baxter Q-operators for the quantum Ruijsenaars hyperbolic system, proving their commutativity and their compatibility with Macdonald difference operators, using advanced hypergeometric identities.

Contribution

It constructs Baxter Q-operators for the system and proves their commutativity, extending the understanding of integrable structures in quantum hyperbolic systems.

Findings

Baxter Q-operators form a commuting family of integral operators.

Q-operators commute with Macdonald difference operators.

The proof relies on generalized hypergeometric identities.

Abstract

We introduce Baxter Q-operators for the quantum Ruijsenaars hyperbolic system. We prove that they represent a commuting family of integral operators and also commute with Macdonald difference operators, which are gauge equivalent to the Ruijsenaars Hamiltonians of the quantum system. The proof of commutativity of the Baxter operators uses a hypergeometric identity on rational functions that generalize Ruijsenaars kernel identities.