Characteristic classes of -bundles and quantum dynamical elliptic R-matrices

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 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 ZN 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.