In this chapter we study the linear representations of the one-parameter Iwahori–Hecke algebras of Section 4.2.2. Our aim is to classify their finite-dimensional representations over an algebraically closed field of characteristic zero in terms of partitions and Young diagrams. As an application, we prove that the reduced Burau representation introduced in Section 3.3 is irreducible. We end the chapter by a discussion of the Temperley–Lieb algebras.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2008 Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Kassel, C., Turaev, V. (2008). Representations of the Iwahori–Hecke Algebras. In: Braid Groups. Graduate Texts in Mathematics, vol 247. Springer, New York, NY. https://doi.org/10.1007/978-0-387-68548-9_5
Download citation
DOI: https://doi.org/10.1007/978-0-387-68548-9_5
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-33841-5
Online ISBN: 978-0-387-68548-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)