Geodesic
On the~$R$-matrix identities related to elliptic anisotropic
Teoretičeskaâ i matematičeskaâ fizika, Tome 213 (2022) no. 2, pp. 268-286

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We propose and prove a set of identities for the elliptic $GL_M$ $R$-matrix (in the fundamental representation). In the scalar case ($M=1$), these are elliptic function identities derived by Ruijsenaars as necessary and sufficient conditions for his kernel identity underlying the construction of integral solutions of quantum spinless Ruijsenaars–Schneider model. In this respect, our result can be regarded as a first step toward constructing solutions of the quantum eigenvalue problem for the anisotropic spin Ruijsenaars model.
Keywords: quantum integrable spin many-body system, spin Ruijsenaars–Schneider model, $R$-matrix identities, kernel identity. 
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     author = {M. G. Matushko and A. V. Zotov},
     title = {On the~$R$-matrix identities related to elliptic anisotropic},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {268--286},
     publisher = {mathdoc},
     volume = {213},
     number = {2},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2022_213_2_a3/}
}
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M. G. Matushko; A. V. Zotov. On the~$R$-matrix identities related to elliptic anisotropic. Teoretičeskaâ i matematičeskaâ fizika, Tome 213 (2022) no. 2, pp. 268-286. http://geodesic.mathdoc.fr/item/TMF_2022_213_2_a3/