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Homological representations of the Iwahori-Hecke algebra

Stephen Bigelow
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Abstract

Representations of the Iwahori-Hecke algebra of type A_{n-1} are equivalent to representations of the braid group B_n for which the generators satisfy a certain quadratic relation. We show how to construct such representations from the natural action of B_n on the homology of configuration spaces of the punctured disk. We conjecture that all irreducible representations of Hecke_n can be obtained in this way, even for non-generic values of q.

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Stephen Bigelow. 2004-12-28. Homological representations of the Iwahori-Hecke algebra. https://arxiv.org/abs/math/0412516

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