Presentation Date:
Location:
Presentation Slides:
It's a well-known theorem of Scopes that if we consider the blocks of FpSm for all m geq 0 with a fixed defect group, they will break into a finite number of Morita equivalence classes. In fact, it was later shown by Chuang and Rouquier that all blocks with a fixed defect group are derived equivalent; from this perspective, one can think of Scopes' theorem as the observation that “most” of Chuang and Rouquier's derived equivalences are induced by Morita equivalences (i.e. are t-exact). I'll discuss how one can organize these equivalences using the combinatorics of affine Lie algebras and extend Scopes' theorem to the other categorical actions appearing in modular representation theory, in particular, to Ariki-Koike algebras, based on the work of Lyle.
