A Kohno-Drinfeld theorem for quantum Weyl groups
A Kohno-Drinfeld theorem for quantum Weyl groups
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量子 Weyl 群的 Kohno-Drinfeld 定理
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发表时间：
2002
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通讯作者：
V. T. Laredo
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作者：
V. T. Laredo
设g是一个复单李代数，g的Cartan子代数h和Weyl群W都是V，V是g的一个有限维表示.在[MTL]中，我们引入了一个新的，W -等变平坦的连接上的值在V和简单的极点沿着根超平面。这种联系依赖于一个参数∈ C，在[TL]中证明了它的单值性等价于Lusztig，Kirillov-Reshetikhin和Soibelman利用量子群Ug在V上的作用所定义的g型辫子群的表示.本文证明了g = sln时的这一猜想.
Let g be a complex, simple Lie algebra with Cartan subalgebra h and Weyl group W and let V be a finite–dimensional representation of g. In [MTL], we introduced a new, W –equivariant flat connection on h with values in V and simple poles along the root hyperplanes. This connection depends upon a parameter ∈ C and it was conjectured in [TL] that its monodromy is equivalent to the representation of the braid group of type g defined by Lusztig, Kirillov–Reshetikhin and Soibelman by using the action of the quantum group U g on V. In this paper, we prove this conjecture for g = sln.