An ABV-packet for GL(16) with two representations

Speaker: Nicole Kitt
Abstract: It is known that not all ABV-packets are Arthur packets, and in particular, that Arthur packets for general linear groups are singletons. This talk concerns, what is believed to be, the smallest known example of an ABV-packet for a general linear group that is not a singleton, and hence is not of Arthur type. Specifically, we have shown that there is an irreducible admissible representation $\pi_{KS}$ of p-adic GL(16) with the property that its ABV-packet contains exactly one other irreducible representation, $\pi_{\psi}$.
The main tool that we use to calculate the ABV-packet for p-adic GL(16) is the functor Ev. In this talk, I will illustrate the geometric methods used to compute this functor. In particular, I will provide a sketch computation of the ABV-packet for GL(16). Before doing so, I will review ABV-packets and Vogan varieties for GL(n). This is joint work with Clifton Cunningham, based on prior joint work with Clifton and Reginald Lybbert; both of which included several enlightening conversations with Andrew Fiori.