Representations of the Iwahori–Hecke Algebras
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.