Flat Connections and Quantum Groups
Quantum Algebra
2009-09-29 v1 Representation Theory
Abstract
We review the Kohno-Drinfeld theorem as well as a conjectural analogue relating quantum Weyl groups to the monodromy of a flat connection D on the Cartan subalgebra of a complex, semi-simple Lie algebra g with poles on the root hyperplanes and values in any g-module V. We sketch our proof of this conjecture when g=sl(n) and when g is arbitrary and V is a vector, spin or adjoint representation. We also establish a precise link between the connection D and Cherednik's generalisation of the KZ connection to finite reflection groups.
Cite
@article{arxiv.math/0205185,
title = {Flat Connections and Quantum Groups},
author = {Valerio Toledano-Laredo},
journal= {arXiv preprint arXiv:math/0205185},
year = {2009}
}
Comments
20 pages. To appear in the Proceedings of the 2000 Twente Conference on Lie Groups, in a special issue of Acta Applicandae Mathematicae