# The rarefied elliptic Bailey lemma and the Yang-Baxter equation

## TL;DR

This paper introduces a new elliptic Bailey lemma based on the rarefied elliptic beta integral, leading to novel solutions of the Yang-Baxter equation through integral operators with elliptic hypergeometric kernels.

## Contribution

It formulates a rarefied elliptic Bailey lemma and derives a new integral operator solution to the Yang-Baxter equation.

## Key findings

- Derived a generalized operator star-triangle relation.
- Presented a new solution to the Yang-Baxter equation.
- Connected elliptic hypergeometric functions with integrable models.

## Abstract

An elliptic Bailey lemma is formulated on the basis of the univariate rarefied elliptic beta integral. It leads to a generalized operator star-triangle relation and a new solution of the Yang-Baxter equation written as an integral operator with a rarefied elliptic hypergeometric kernel.