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This article is cited in 7 scientific papers (total in 7 papers)
Higher-order analogues of the unitarity condition for quantum $R$-matrices
A. V. Zotov Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
Abstract:
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.
Received: 08.11.2015 Revised: 18.12.2015
Citation:
A. V. Zotov, “Higher-order analogues of the unitarity condition for quantum $R$-matrices”, TMF, 189:2 (2016), 176–185; Theoret. and Math. Phys., 189:2 (2016), 1554–1562
Linking options:
https://www.mathnet.ru/eng/tmf9097https://doi.org/10.4213/tmf9097 https://www.mathnet.ru/eng/tmf/v189/i2/p176
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Abstract page: | 364 | Full-text PDF : | 119 | References: | 51 | First page: | 11 |
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