Bernoulli Lecture - Representation theory of symmetric groups and categorification   15 December 2016

17:15 - 18:15
Room : BI A0 448

Lecturer

Alexander Kleshchev, University of Oregon

We review recent (~20 years) advances in representation theory of symmetric groups with the emphasis on categorification techniques.

Branching rules describe restrictions of irreducible representations of a symmetric group to a smaller symmetric group. Studying branching rules leads one to a categorification idea: restriction and induction functors yield a categorical action of certain Lie algebras on representation categories of symmetric groups. The corresponding action of the Weyl group lifts to a derived equivalence between the blocks of the symmetric groups (Chuang-Rouquier). Connections with Khovanov-Lauda-Rouquier algebras tie the categorical actions to quantum groups.

In the very end, we present a joint result with Anton Evseev, which describes every block of a symmetric group up to derived equivalence as a certain Turner double algebra. This description was conjectured by Will Turner. Turner doubles are Schur-algebra-like 'local' objects, which replace wreath products of Brauer tree algebras in the context of the Broué abelian defect group conjecture for blocks of symmetric groups with non-abelian defect groups.

Most of the ideas presented in the talk hold much more generally, but we stick mostly to symmetric groups to make presentation non-technical.

Name University Dates of visit
Alexander Kleshchev University of Oregon 15/12/2016 - 15/12/2016
Total Guests : 1
Name University Dates of visit
Total Guests : 0