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

Abstract

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

arXiv comment6 pages, minor changes

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Cited by in corpus (5)

• Field theory generalizations of two-body Calogero-Moser models in the form of Landau-Lifshitz equations
• Elliptic generalization of integrable q-deformed anisotropic Haldane-Shastry long-range spin chain
• Lax equations for relativistic $\mathrm{GL}(NM,\mathbb{C})$ Gaudin models on elliptic curve
• Supersymmetric generalization of q-deformed long-range spin chains of Haldane-Shastry type and trigonometric GL(N|M) solution of associative Yang-Baxter equation
• Multi-pole extension for elliptic models of interacting integrable tops