q-Schur algebras, Wedderburn decomposition and James' conjecture

In this talk we present a new construction of a Wedderburn basis for

the generic q-Schur algebra using the Du-Kazhdan-Lusztig basis. We show

that this gives rise to a new view on the Du-Lusztig homomorphism to the

asymptotic algebra. At the end we explain a potential plan for an attack

on James' conjecture using a reformulation by Meinolf Geck.

The talk starts with a gentle recollection of facts about

Iwahori-Hecke-Algebras of type A and q-Schur algebras and aims to be

accessible to people who are not (yet) experts in the representation

theory of q-Schur algebras.

All this is joint work with Olivier Brunat (Bochum).