Braid groups and Iwahori-Hecke algebras

Details Braid groups and Iwahori-Hecke algebras Braid groups and Iwahori-Hecke algebras

2005-05-04

arxiv.org/abs/math/0505064v1

Mathematics

Geometric Topology

15 pages, 4 figures

Scientific paper

This article was submitted to a volume under preparation, with Benson Farb as the editor, on the topic of open problems in surface mapping class groups. The braid group B_n is the mapping class group of an n-times punctured disk. The Iwahori-Hecke algebra H_n is a quotient of the braid group algebra of B_n by a quadratic relation in the standard generators. We discuss how to use H_n to define the Jones polynomial of a knot or link. We also summarize the classification of the irreducible representations of H_n. We conclude with some directions for future research that would apply mapping class group techniques to questions related to H_n.

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