Characteristic Classes of SL(N)-Bundles and Quantum Dynamical Elliptic R-Matrices
Mathematical Physics
2013-07-12 v1 High Energy Physics - Theory
math.MP
Representation Theory
Exactly Solvable and Integrable Systems
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.
Cite
@article{arxiv.1208.5750,
title = {Characteristic Classes of SL(N)-Bundles and Quantum Dynamical Elliptic R-Matrices},
author = {A. Levin and M. Olshanetsky and A. Smirnov and A. Zotov},
journal= {arXiv preprint arXiv:1208.5750},
year = {2013}
}
Comments
27 pages