11:30
11:30
q-Schur algebras, Wedderburn decomposition and James' conjecture
Abstract
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).
What does a generic measure looks like?
Abstract
The talk will give two entirely different answers to the question asked in the title of the talk. A topological answer will be based on the classical notion of Baire category. A measure theoretical answer will be based on the much newer notion of prevalence/shyness.