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