The Arthur-Packet Support Equality for Real Reductive Groups

Abstract

Let ψ be a real Arthur parameter and let ψ₂ be the unipotent parameter in a fixed Jordan decomposition. Adams, Ionov, Mason-Brown, and Vogan proved that the microlocal packet of ψ is contained in the support of the two-step Jordan induction of the packet of ψ₂, and conjectured equality. We prove the reverse inclusion. The argument first passes to a sufficiently positive translate, where the relevant connected components of the ABV spaces have a common flag-variety model. Perverse dévissage reduces the problem to a singular-support implication, which follows from the incidence calculation underlying the AIMV microstalk comparison. Coherent continuation for individual packet members then returns the result to the original parameter.

Topics

• Representation theory
• Langlands program
• Arthur packets
• ABV packets
• Real reductive groups
• Microlocal geometry
• Jordan induction