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This article is cited in 1 scientific paper (total in 1 paper)
Higher-rank generalization of the 11-vertex rational $R$-matrix: IRF–vertex relations and the associative Yang–Baxter equation
K. R. Atalikovab, A. V. Zotovab a Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
b National Research Centre "Kurchatov Institute", Moscow, Russia
Abstract:
We study the $\text{GL}_N$ rational $R$-matrix, which turns into the $11$-vertex $R$-matrix in the $N=2$ case. First, we describe its relations to dynamical and semidynamical $R$-matrices using the IRF–vertex type transformations. As a by-product, a new explicit form of the $\text{GL}_N$ $R$-matrix is derived. Next, we prove the quantum and the associative Yang–Baxter equations. A set of other $R$-matrix properties and $R$-matrix identities are also proved.
Keywords:
rational $R$-matrix, IRF–vertex relations, associative Yang–Baxter equation.
Received: 04.03.2023 Revised: 04.03.2023
Citation:
K. R. Atalikov, A. V. Zotov, “Higher-rank generalization of the 11-vertex rational $R$-matrix: IRF–vertex relations and the associative Yang–Baxter equation”, TMF, 216:2 (2023), 203–225; Theoret. and Math. Phys., 216:2 (2023), 1083–1103
Linking options:
https://www.mathnet.ru/eng/tmf10488https://doi.org/10.4213/tmf10488 https://www.mathnet.ru/eng/tmf/v216/i2/p203
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