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Representations of the Iwahori-Hecke algebra of type An 1 are equivalent to representations of the braid group Bn for which the genera- tors satisfy a certain quadratic relation. We show how to construct such representations from the natural action of Bn on the homology of config- uration spaces of the punctured disk. We conjecture that all irreducible representations of Hn can be obtained in this way, even for non-generic values of q. AMS Classification 20C08; 20F36, 57M07

Homological representations of the Iwahori–Hecke algebra