# GL(NM) quantum dynamical $R$-matrix based on solution of the associative Yang-Baxter equation

## TL;DR

This paper constructs a new class of dynamical R-matrices for GL(NM) using solutions of the associative Yang-Baxter equation, unifying and extending known elliptic and vertex R-matrices.

## Contribution

It introduces a novel GL(NM)-valued dynamical R-matrix derived from associative Yang-Baxter solutions, generalizing Felder's and Baxter-Belavin's R-matrices.

## Key findings

- Reproduces Felder's R-matrix for N=1
- Provides elliptic and degenerate R-matrices for M=1
- Unifies different types of R-matrices under a common framework

## Abstract

In this letter we construct ${\rm GL}_{NM}$-valued dynamical $R$-matrix by means of unitary skew-symmetric solution of the associative Yang-Baxter equation in the fundamental representation of ${\rm GL}_{N}$. In $N=1$ case the obtained answer reproduces the ${\rm GL}_{M}$-valued Felder's $R$-matrix, while in the $M=1$ case it provides the ${\rm GL}_{N}$ $R$-matrix of vertex type including the Baxter-Belavin's elliptic one and its degenerations.