A Kohno-Drinfeld theorem for quantum Weyl groups
Valerio Toledano Laredo
Source: Duke Math. J. Volume 112, Number 3 (2002), 421-451.
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 $\mathfrak {g}=\mathfrak {sl}\sb n$.
Primary Subjects: 17B37
Secondary Subjects: 16W35, 20F36, 32G34
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MR1896470
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Zentralblatt MATH identifier:
1016.17010
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