Distinguished regular supercuspidal representations

Abstract

Based on recent work of Kaletha, we apply Hakim--Murnaghan's result to study distinguished regular supercuspidal representations of tamely ramified reductive $p$-adic groups. Assuming $p$ is sufficiently large, we obtain a necessary and sufficient condition for regular supercuspidal representations to be distinguished. We also investigate the relation between the distinction problem and the Langlands functoriality, and confirm a conjecture of Lapid for regular depth-zero or epipelagic supercuspidal representations.

Final version, to appear in Mathematische Annalen

References in corpus (2)

• A `relative' local Langlands correspondence
• Representations of reductive groups distinguished by symmetric subgroups

Cited by in corpus (1)

• Theta lifts and distinction for regular supercuspidal representations