K. R. Atalikov, A. V. Zotov, “Higher-rank generalization of the 11-vertex rational <nobr>$R$</nobr>-matrix: IRF–vertex relations and the associative Yang–Baxter equation”, TMF, 2023, Volume 216, Number 2,Pages <nobr>203

This article is cited in 3 papers

Higher-rank generalization of the 11-vertex rational $R$-matrix: IRF–vertex relations and the associative Yang–Baxter equation

K. R. Atalikov^ab, A. V. Zotov^ab

^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

DOI: 10.4213/tmf10488