Abstract: This talk concerns work in progress on a generalization of the notion of local Arthur packets from Arthur-type representations of classical groups over $p$-adic fields to all admissible representations of all connected reductive algebraic groups over p-adic fields. In this talk our goal is much more modest: to report on this project for unipotent representations of the exceptional group G_2(F) for a p-adic field F. We will explain how to use the microlocal geometry of the moduli space of unramified Langlands parameters to compute what we call Adams-Barbasch-Vogan packets, or ABV-packets for short, for all unipotent representations of G_2(F) and how to find the packet coefficients that are required to build stable distributions from ABV-packets. This talk will focus on the case that is the more interesting geometrically and will include a discussion of unipotent representations that are not of Arthur type. We will argue that ABV-packets provide the correct extension of the notion of Arthur packets by explaining that the packet coefficients satisfy expected conditions coming from endoscopic character identities.

Joint work with Andrew Fiori and Qing Zhang, based on earlier joint work with Andrew Fiori, Ahmed Moussaoui, James Mracek and Bin Xu, which in turn is based on earlier work by David Vogan.

For the introductory slides on this topic, please see: http://www.fields.utoronto.ca/sites/default/files/uploads/Introduction_1...

For an introductory lecture on this topic, please see: https://youtu.be/ad85GSAVAK4