An infinite family of higher-order difference operators that commute with Ruijsenaars operators of type $A$

TL;DR

This paper introduces an infinite family of higher-order difference operators that commute with elliptic Ruijsenaars operators of type A, expanding the understanding of their algebraic structure and interrelations.

Contribution

It presents a new infinite family of commuting difference operators related to elliptic Ruijsenaars operators via a Wronski-type formula, advancing the theory of integrable systems.

Findings

Established a new family of commuting difference operators

Connected these operators with Ruijsenaars' operators through a Wronski-type relation

Enhanced the algebraic framework of elliptic integrable systems

Abstract

We introduce a new infinite family of higher-order difference operators that commute with the elliptic Ruijsenaars difference operators of type $A$. These operators are related with Ruijsenaars' operators through a formula of Wronski type.