Algebra Seminar

The Iwahori-Hecke algebra H of type A is a deformation of the group algebra of the symmetric group. The representation theory of H closely mirrors that of the symmetric group; indeed its irreducible representation were first constructed by Dipper and James using what amounted to brute force adaptations of the `classical' theory.

In this talk we will sketch the proof of a more elegant construction due to Murphy which builds upon Graham and Lehrer's theory of cellular algebras. We will then go on to show how these results can be "lifted" to construct the irreducible representations of the q-Schur algebras (using recent work of Dipper, James and myself and related to work of Du and Scott).