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.

Categories: math.QA hep-th math-ph math.MP nlin.SI

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