Homological representations of the Iwahori-Hecke algebra

2004/12/28 by Stephen Bigelow
Mathematics · #math.QA #math.GT #msc:20C08 #msc:20F36 #msc:57M07

paper · pdf

published as Geom. Topol. Monogr. 7 (2004) 493-507 · Published by Geometry and Topology Monographs at http://www.maths.warwick.ac.uk/gt/GTMon7/paper16.abs.html

arxiv created 2004/12/28 · arxiv updated 2009/12/01

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.

Related

• Representations of braid groups
• Braid groups and Iwahori-Hecke algebras
• The representation type of Hecke algebras of type B
• Remarks on the faithfulness of the Jones representations
• The homological content of the Jones representations at q = -1