Homological representations of the Iwahori-Hecke algebra

Details Homological representations of the Iwahori-Hecke algebra Homological representations of the Iwahori-Hecke algebra

2004-12-28

arxiv.org/abs/math/0412516v1

Geom. Topol. Monogr. 7 (2004) 493-507

Mathematics

Quantum Algebra

Published by Geometry and Topology Monographs at http://www.maths.warwick.ac.uk/gt/GTMon7/paper16.abs.html

Scientific paper

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.

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