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arXiv · 1208.5750

Characteristic Classes of SL(N)-Bundles and Quantum Dynamical Elliptic R-Matrices

A. Levin·M. Olshanetsky·A. Smirnov·A. Zotov
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Abstract

We discuss quantum dynamical elliptic R-matrices related to arbitrary complex simple Lie group G. They generalize the known vertex and dynamical R-matrices and play an intermediate role between these two types. The R-matrices are defined by the corresponding characteristic classes describing the underlying vector bundles. The latter are related to elements of the center Z(G) of G. While the known dynamical R-matrices are related to the bundles with trivial characteristic classes, the Baxter-Belavin-Drinfeld-Sklyanin vertex R-matrix corresponds to the generator of the center Z_N of SL(N). We construct the R-matrices related to SL(N)- bundles with an arbitrary characteristic class explicitly and discuss the corresponding IRF models.

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A. Levin, M. Olshanetsky, A. Smirnov, A. Zotov. 2012-08-28. Characteristic Classes of SL(N)-Bundles and Quantum Dynamical Elliptic R-Matrices. https://doi.org/10.1088/1751-8113/46/3/035201

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