Augmented branching rules for symmetric groups in characteristic two

by Robert Muth ((Duquesne University Pittsburgh))

Friday Jan 10, 2025, 2:15 PM → 3:15 PM Europe/Berlin

Endenicher Allee 60, Nebengebäude/1.008 - Seminarraum (Mathezentrum)

The representation theory of the symmetric group $S_n$ in characteristic two (or more generally, Hecke algebras at a second root of unity) can be approached from a number of directions; classically, via Specht modules and the cellular structure of $S_n$, or more recently via the larger stratified structure of the KLR algebra of type $A_1^{(1)}$. I will discuss a combinatorial bridge between between these two perspectives. This bridge allows one to augment Kleshchev’s famous branching graph for $S_n$ with a richer set of edges corresponding to induction/restriction by cuspidal modules for positive roots of type $A_1^{(1)}$, and yields new analogues of James’ regularization theorem for Specht modules in this setting as well.