Speaker
Description
Arthur packets are sets containing irreps that form constituents of important classes of automorphic representations. ABV-packets, named after Jeff Adams, Dan Barbasch, and David Vogan, are proposed generalizations to local Arthur packets for archimedean groups. They arise out of a geometric perspective on the local Langlands correspondence involving microlocal analysis on moduli spaces of Langlands parameters. Vogan gave an analogous description for the non-archimedean case, which was then adapted by Cunningham et al. The proposal that an ABV-packet for a Langlands parameter of Arthur-type coincides with the corresponding local Arthur packet is stated as Vogan's conjecture by Cunningham et al in their adaptation. This talk aims to report on the progress of Vogan's conjecture for $p$-adic general linear, odd special orthogonal, and symplectic groups.