Flat Connections and Quantum Groups
Author: Toledano Laredo V.1
Source: Acta Applicandae Mathematicae, Volume 73, Numbers 1-2, August 2002 , pp. 155-173(19)
Publisher: Springer
Abstract:
We review the KohnoDrinfeld theorem and a conjectural analogue relating quantum Weyl groups to the monodromy of a flat connection
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=sln or when g is arbitrary and V is a vector, spin or adjoint representation. We also establish a precise link between the connection
C and Cherednik's generalisation of the KnizhnikZamolodchikov connection to finite reflection groups.
Keywords: braid groups; monodromy; quantum groups; quantum Weyl groups; KohnoDrinfeld 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

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