Flat Connections and Quantum Groups

Author: Toledano Laredo V.

Source: Acta Applicandae Mathematicae, Volume 73, Numbers 1-2, August 2002 , pp. 155-173(19)

Publisher: Springer

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Abstract:

We review the Kohno–Drinfeld theorem and a conjectural analogue relating quantum Weyl groups to the monodromy of a flat connection nabla _C 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 for the cases when g=sl_n or when g is arbitrary and V is a vector, spin or adjoint representation. We also establish a precise link between the connection nabla _C and Cherednik's generalisation of the Knizhnik–Zamolodchikov connection to finite reflection groups.

Keywords: braid groups; monodromy; quantum groups; quantum Weyl groups; Kohno–Drinfeld theorem

Language: English

Document Type: Research article

Affiliations: 1: Institut de Mathématiques de Jussieu, UMR 7586, Case 191, 175 rue du Chevaleret, 75013 Paris, France. e-mail: toledano@math.jussieu.fr

Publication date: 2002-08-01