Flat Connections and Quantum Groups

Details Flat Connections and Quantum Groups Flat Connections and Quantum Groups

2002-05-16

arxiv.org/abs/math/0205185v1

Acta Appl. Math. 73 (2002), 155-173

Mathematics

Quantum Algebra

20 pages. To appear in the Proceedings of the 2000 Twente Conference on Lie Groups, in a special issue of Acta Applicandae Mat

Scientific paper

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.

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