Arthur packets for G(2) and perverse sheaves on cubics

Abstract: This talk demonstrates a non-invasive procedure that calculates Arthur packets, their associated stable distributions and Langlands-Shelstad transfers, without direct use of endoscopy, using certain unipotent representations of the split p-adic exceptional group G(2) as examples. In the case at hand, this procedure relies on a study of the category of GL(2)-equivariant perverse sheaves on the moduli space of homogeneous cubics in two variables, which is perhaps of independent interest. Specifically, we find the Fourier transform and the microlocalization of the simple objects in this category, and convert that into information about the Aubert involution and stable distributions attached to Arthur packets. This is joint work with Andrew Fiori and Qing Zhang, based on earlier joint work with Andrew Fiori, Ahmed Moussaoui, James Mracek and Bin Xu, which is based on earlier work by David Vogan, sadly, not joint.

representation theory

Audience: researchers in the topic

MIT Lie groups seminar

Series comments: Description: Research seminar on Lie groups

This seminar will take place entirely online: Zoom Meeting Link. You should be able to watch live video at this link. Your microphone will be muted, but you are welcome to unmute it (microphone icon on the lower left of the Zoom window, perhaps visible only when you put your mouse near there) to ask a question.