Algebra Seminar

In this talk I will describe the circle of ideas behind the classification of the irreducible representations of the affine Hecke algebras of type A (over an arbitrary field). The proof involves the interplay between the geometry of quivers, representations of quantum groups and the the combinatorics of the Ariki-Koike algebras.

The talk will begin with an elementary discussion of the `Specht modules' and branching rules for these algebras. This leads to the the definition of the Fock space, which is naturally a module for the Kac-Moody algebra of an affine special linear group. The final stage involves introducing Lusztig's canonical basis at which point the theory becomes very difficult and also very interesting.