Geodesic
Higher-order analogues of the unitarity condition for quantum $R$-matrices
Teoretičeskaâ i matematičeskaâ fizika, Tome 189 (2016) no. 2, pp. 176-185 Cet article a éte moissonné depuis la source Math-Net.Ru

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We derive a family of $n$th-order identities for quantum $R$-matrices of the Baxter–Belavin type in the fundamental representation. The set of identities includes the unitarity condition as the simplest case $(n=2)$. Our study is inspired by the fact that the third-order identity provides commutativity of the Knizhnik–Zamolodchikov–Bernard connections. On the other hand, the same identity yields the $R$-matrix-valued Lax pairs for classical integrable systems of Calogero type, whose construction uses the interpretation of the quantum $R$-matrix as a matrix generalization of the Kronecker function. We present a proof of the higher-order scalar identities for the Kronecker functions, which is then naturally generalized to $R$-matrix identities.
Keywords: classical integrable system, $R$-matrix Lax representation, duality. 
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A. V. Zotov. Higher-order analogues of the unitarity condition for quantum $R$-matrices. Teoretičeskaâ i matematičeskaâ fizika, Tome 189 (2016) no. 2, pp. 176-185. http://geodesic.mathdoc.fr/item/TMF_2016_189_2_a1/

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