#### 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.

Notes on file formats
Stephen Bigelow

Department of Mathematics, University of California at Santa Barbara

California 93106, USA

Email: bigelow@math.ucsb.edu

GTM home page

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