EVENT DETAILS AND ABSTRACT

Title: Mod p representations of $p$-adic ${\rm GL}(3)$
Speaker: Rachel Ollivier
Speaker Info: Columbia University
Brief Description:
Special Note: There will be a preseminar talk for graduate students at 11 am in Lunt 101.
Abstract:

Let $p$ be a prime number, $q$ a power of $p$, and $F$ a $p$-adic field with residue field $\mathbb F_q$. We give an overview of the functorial links between Hecke modules and representations of ${\rm GL}(3,\mathbb F_q)$ in characteristic $p$. Using properties of the affine building of ${\rm PGL}(3,F)$, we describe the analogous links for ${\rm GL}(3,F)$, and draw information about the supersingular representations of ${\rm GL}(3,F)$ from the knowledge of the supersingular Hecke modules.