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arXiv:1511.02468 · Theoretical and Mathematical Physics

Higher-order analogues of the unitarity condition for quantum R-matrices

Andrei Vladimirovich Zotov

Published Nov 1, 2016• 9 citations
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Abstract

We derive a family of nth-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.

DOI
10.1134/s0040577916110027

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Matrix representations of BCn{\rm BC}_nBCn​ associative Yang--Baxter equations and related long-range spin chains
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