Homological representations of the Hecke algebra
Homological representations of the Hecke algebra
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赫克代数的同调表示
DOI：
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发表时间：
1990
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通讯作者：
R. Lawrence
中科院分区：
文献类型：
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作者：
R. Lawrence
本文给出了与2行Young图有关的Hecke代数的Thean(1)-级数表示的一种拓扑结构。这种结构给出了从具有自然平坦连接的向量丛获得的单行表示的表示。向量丛的纤维是C中点的位形空间的同调空间，具有合适的扭曲局部系数系。它还表明，这种构造与土屋和Kanie的工作有密切的对应，他们从P1上的共形场论中的n点函数的单行构造了Hecke代数表示。这项工作对于一元Jones多项式具有重要意义，它可以用与2行Young图相关的Iwahori-Hecke代数的特征来表示；它引起了Jones多项式的拓扑描述，这将在其他地方讨论[L2]。
In this paper a topological construction of representations of theAn(1)-series of Hecke algebras, associated with 2-row Young diagrams will be given. This construction gives the representations in terms of the monodromy representation obtained from a vector bundle on which there is a natural flat connection. The fibres of the vector bundle are homology spaces of configuration spaces of points in C, with a suitable twisted local coefficient system. It is also shown that there is a close correspondence between this construction and the work of Tsuchiya and Kanie, who constructed Hecke algebra representations from the monodromy ofn-point functions in a conformal field theory onP1. This work has significance in relation to the one-variable Jones polynomial, which can be expressed in terms of characters of the Iwahori-Hecke algebras associated with 2-row Young diagrams; it gives rise to a topological description of the Jones polynomial, which will be discussed elsewhere [L2].