Theta lifts and distinction for regular supercuspidal representations

Abstract

This article has a twofold purpose. First, by recent works of Kaletha and Loke–Ma, we give an explicit description of the local theta correspondence between regular supercuspidal representations in the equal rank symplectic-orthogonal case. Second, based on this description, we show that the local theta correspondence preserves distinction with respect to unramified Galois involutions.