An upper bound for wavefront sets of admissible representations of p-adic groups

Abstract: The Vogan conjecture states that local Arthur packets match ABV-packets for L-parameters of Arthur type. Thus, it is expected that the properties of local Arthur packets should hold for the corresponding ABV-packets, and vice versa. In the first part of this talk, I will recall some basic properties of these packets, and state the closure ordering conjecture on local Arthur pacekts and Aubert-Zelevinsky dual conjecture on ABV-packets. In the second part, I will introduce a new conjecture on upper bounds of wavefront set, Jiang's conjecture on wavefront set for local Arthur packets and for ABV-packets. I will show that these three conjectures are all equivalent assuming the two conjectures in the first part hold, and reduce these conjectures to the anti-discrete case. This is a joint work with Alexander Hazeltine, Baiying Liu and Freydoon Shahidi.

algebraic geometrynumber theoryrepresentation theory

Audience: researchers in the topic

Canadian Rockies Representation Theory

Series comments: Topics include, but are not limited to, geometric and categorical aspects of the Langlands Programme. Please write to Jose Cruz for zoom instructions.