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15 April 2002 A Kohno-Drinfeld theorem for quantum Weyl groups
Valerio Toledano Laredo
Duke Math. J. 112(3): 421-451 (15 April 2002). DOI: 10.1215/S0012-9074-02-11232-0

Abstract

Let $\mathfrak {g}$ be a complex, simple Lie algebra with Cartan subalgebra $\mathfrak {h}$ and Weyl group $W$. In [MTL], we introduced a new, $W$-equivariant flat connection on $\mathfrak {h}$ with simple poles along the root hyperplanes and values in any finite-dimensional $\mathfrak {g}$-module $V$. It was conjectured in [TL] that its monodromy is equivalent to the quantum Weyl group action of the generalised braid group of type $\mathfrak {g}$ on $V$ obtained by regarding the latter as a module over the quantum group $U\sb \hbar\mathfrak {g}$. In this paper, we prove this conjecture for $\mathfrak {g}=\mathfrak {sl}\sb n$.

Citation

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Valerio Toledano Laredo. "A Kohno-Drinfeld theorem for quantum Weyl groups." Duke Math. J. 112 (3) 421 - 451, 15 April 2002. https://doi.org/10.1215/S0012-9074-02-11232-0

Information

Published: 15 April 2002
First available in Project Euclid: 18 June 2004

zbMATH: 1016.17010
MathSciNet: MR1896470
Digital Object Identifier: 10.1215/S0012-9074-02-11232-0

Subjects:
Primary: 17B37
Secondary: 16W35 , 20F36 , 32G34

Rights: Copyright © 2002 Duke University Press

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Vol.112 • No. 3 • 15 April 2002
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