Volume 7 (2004)

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Homological representations of the Iwahori–Hecke algebra

Stephen Bigelow

Geometry & Topology Monographs 7 (2004) 493–507

DOI: 10.2140/gtm.2004.7.493

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 Hn can be obtained in this way, even for non-generic values of q.

Keywords

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

Mathematical Subject Classification

Primary: 20C08

Secondary: 20F36, 57M07

Publication

Received: 9 September 2003
Revised: 25 May 2004
Accepted: 10 May 2004
Published: 13 December 2004

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