The Arthur-Packet Support Equality for Real Reductive Groups

Abstract

Let $ψ$ be a real Arthur parameter and let $ψ_2$ 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 $ψ_2$, 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 devissage 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.