Simple supercuspidal L-packets of quasi-split classical groups

TL;DR

This paper explicitly determines L-packets of simple supercuspidal representations for quasi-split classical groups over p-adic fields, using character computations and endoscopic relations, advancing the local Langlands correspondence understanding.

Contribution

It provides an explicit description of L-packets and their L-parameters for quasi-split classical groups, under the assumption p ≠ 2, through character analysis and endoscopy.

Findings

Explicit L-packets for quasi-split classical groups identified

Character formulas for simple supercuspidal representations computed

Endoscopic character relations verified for these groups

Abstract

In this paper, for quasi-split classical groups over p-adic fields, we determine the L-packets consisting of simple supercuspidal representations and their corresponding L-parameters, under the assumption that p is not equal to 2. The key is an explicit computation of characters of simple supercuspidal representations and the endoscopic character relation, which is a characterization of the local Langlands correspondence for quasi-split classical groups.