# KZ equations and Bethe subalgebras in generalized Yangians related to compatible R-matrices

## TL;DR

This paper introduces generalized Yangians derived from compatible braidings, constructs Bethe subalgebras within them, and explores their relation to KZ equations, expanding the algebraic framework of quantum integrable systems.

## Contribution

It defines new generalized Yangian algebras and constructs commutative Bethe subalgebras, extending prior work on compatible braidings and symmetric polynomials.

## Key findings

- Bethe subalgebras are generated in generalized Yangians.
- Analogues of KZ equations are formulated in this new setting.
- The constructed subalgebras commute, indicating integrability.

## Abstract

The notion of compatible braidings was introduced by Isaev, Ogievetsky and Pyatov. On the base of this notion they defined certain quantum matrix algebras generalizing the RTT algebras and Reflection Equation ones. They also defined analogs of some symmetric polynomials in these algebras and showed that these polynomials generate commutative subalgebras, called Bethe. By using a similar approach we introduce certain new algebras called generalized Yangians and define analogs of some symmetric polynomials in these algebras. We claim that they commute with each other and thus generate a commutative Bethe subalgebra in each generalized Yangian. Besides, we define some analogs (also arising from couples of compatible braidings) of the Knizhnik-Zamolodchikov equation--classical and quantum.