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

TL;DR

This paper introduces a new class of quantum dynamical elliptic R-matrices associated with SL(N)-bundles characterized by arbitrary classes, extending known R-matrices and exploring their applications in IRF models.

Contribution

It constructs explicit R-matrices for SL(N)-bundles with arbitrary characteristic classes, generalizing existing models and linking them to vector bundle topology.

Findings

Explicit construction of R-matrices for SL(N) with arbitrary characteristic classes

Extension of known dynamical R-matrices to more general bundle classes

Discussion of IRF models related to these new 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 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.