Geometry & Topology Monographs, Vol. 7 (2004),
Proceedings of the Casson Fest,
Paper no. 16, pages 493--507.

Homological representations of the Iwahori-Hecke algebra

Stephen Bigelow

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.

Keywords. Iwahori, Hecke algebra, representation, braid group, configuration space, homology

AMS subject classification. Primary: 20C08. Secondary: 20F36, 57M07.

E-print: arXiv:math.QA/0412516

Submitted to GT on 9 September 2003. (Revised 25 May 2004.) Paper accepted 10 May 2004. Paper published 13 December 2004.

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Stephen Bigelow
Department of Mathematics, University of California at Santa Barbara
California 93106, USA

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