Programm des Emmy-Noether-Seminars

Fri, 16.06.2017, 14:30

End:
Fri, 16.06.2017, 15:30
Sheaves on the alcoves and modular representations
Emmy-Noether-Seminar

Speaker: Peter Fiebig (FAU)
Room: 04.363

I'll report on a joint project with Martina Lanini. The project is meant to give a new perspective on the problem of calculating irreducible characters of reductive algebraic groups in positive characteristics. Given a finite root system R and a field k we introduce an exact category C of sheaves on the partially ordered set of alcoves associated with R, and we show that the indecomposable projective objects in C encode the aforementioned characters. The category is way easier to understand than the representation theory of the group, and it can be thought of as a periodic modular generalization of the category of Soergel bimodules.