Geodesic
Higher-rank generalization of the 11-vertex rational $R$-matrix: IRF--vertex relations and the~associative Yang--Baxter equation
Teoretičeskaâ i matematičeskaâ fizika, Tome 216 (2023) no. 2, pp. 203-225

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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.
Mots-clés : rational $R$-matrix, IRF–vertex relations
Keywords: associative Yang–Baxter equation. 
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     author = {K. R. Atalikov and A. V. Zotov},
     title = {Higher-rank generalization of the 11-vertex rational $R$-matrix: {IRF--vertex} relations and the~associative {Yang--Baxter} equation},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {203--225},
     publisher = {mathdoc},
     volume = {216},
     number = {2},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2023_216_2_a0/}
}
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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. Teoretičeskaâ i matematičeskaâ fizika, Tome 216 (2023) no. 2, pp. 203-225. http://geodesic.mathdoc.fr/item/TMF_2023_216_2_a0/