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

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.