Hyohe Miyachi (University of Bristol)

Friday 6th October, 12.05-12.55pm, Carslaw 373

Rouquier blocks and runner removal Morita equivalences

In my talk I would like to talk about representation theory of symmetric groups, GL_n(F_q), Iwahori-Hecke algebras of type A and their q-Schur algebras at roots of unity. (Here, F_q is a finite field. We suppose that a prime l doesn't divide q. We consider l-modular representations of GL_n(F_q).)

First I'd like to talk about (unipotent) Rouquier blocks in GL_n(F_q), which is based on my thesis. Here, I shall only give you a rouqh survey on these Rouquier blocks. Possibly, I might talk about a joint work with Bernard Leclerc about Fock space as a very closely related topic.

Second, I'd like to talk about a joint work with Joseph Chuang. The focus in the second part is to compare module categories of Hecke algebras at different roots of unity. The result even works for any blocks at any roots of unity in positive characteristics with some suitable assumptions and has some applications for James' conjecture which is consistent with Lusztig's character formula conjecture for type A. Our method for the new results is based on the knowledge of Rouquier block algebras and derived equivalences of block algebras in Hecke algebras in terms of Chuang-Rouquier's sl₂-categorifications and perverse Morita equivalences.