Distinction of regular depth-zero supercuspidal L-packets

TL;DR

This paper investigates the conditions of Prasad's conjecture within the relative Langlands program, specifically confirming necessary conditions for regular depth-zero supercuspidal L-packets under certain assumptions.

Contribution

It provides the first verification of necessary conditions in Prasad's conjecture for a specific class of supercuspidal L-packets in the relative Langlands framework.

Findings

Confirmed necessary conditions for Prasad's conjecture in the regular depth-zero case

Advances understanding of the relative Langlands program for Galois symmetric spaces

Supports the broader conjectural framework with specific case verification

Abstract

In this paper, we study the relative Langlands program formulated by Dipendra Prasad for Galois symmetric spaces. Under certain assumptions, we confirm the necessary conditions in Prasad's conjecture for regular depth-zero supercuspidal L-packets.