[OS Reps] Defect zero block enumeration

In finite group theory, modular representations are assembled into blocks. A famous result states that, up to a few characteristic 2 and 3 exceptions, every finite simple group has a defect 0 block (i.e., a singleton block).

In this talk, I will explain how to establish similar results in two different directions: for unipotent representations of finite classical groups, and for representations of Hecke algebras. In fact, in our context, blocks will be labelled by certain (multi)partitions called cores, and our entire approach will become combinatorial.

This is based on joint work with Emily Norton, Nathan Chapelier, Nicolas Jacon, Cédric Lecouvey and Sylvie Corteel.