Theta lifts and distinction for regular supercuspidal representations

TL;DR

This paper explicitly describes the local theta correspondence for regular supercuspidal representations in the symplectic-orthogonal case and proves that this correspondence preserves distinction under unramified Galois involutions.

Contribution

It provides an explicit description of the local theta correspondence for regular supercuspidal representations and demonstrates its preservation of distinction under unramified Galois involutions.

Findings

Explicit description of local theta correspondence for regular supercuspidal reps

Preservation of distinction under unramified Galois involutions

Advances understanding of theta lifts in representation theory

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.