The Arthur-Packet Support Equality for Real Reductive Groups

Abstract

Let $\psi$ be a real Arthur parameter and let ${\psi }_2$ be the unipotent parameter in a fixed Jordan decomposition. Adams, Ionov, Mason-Brown, and Vogan proved that the microlocal packet of $\psi$ is contained in the support of the two-step Jordan induction of the packet of ${\psi }_2$, 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.

14 pages. Comments welcome