
School of Mathematics and Statistics
Andrew Mathas
University of Sydney
The modular representations of ArikiKoike algebras.
Friday 29th January, 121pm, Carslaw 375.
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 ArikiKoike
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 KacMoody 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.
