Epipelagic Langlands parameters and L-packets for unitary groups

TL;DR

This paper explicitly computes the Local Langlands Correspondence for epipelagic supercuspidal representations of unitary groups, revealing simplifications in L-packets related to new invariants introduced by Kaletha.

Contribution

It provides explicit calculations of the Local Langlands Correspondence for a specific class of supercuspidal representations, highlighting simplifications in L-packets due to new invariants.

Findings

Explicit formulas for Local Langlands Correspondence of epipelagic representations

Identification of simplifications in L-packets related to toral invariant and admissible L-embedding

Enhanced understanding of supercuspidal representations of unitary groups

Abstract

Reeder and Yu have recently given a new construction of a class of supercuspidal representations called epipelagic representations. We explicitly calculate the Local Langlands Correspondence for certain families of epipelagic representations of unitary groups, following the general construction of Kaletha [Kal15]. The interesting feature of our computation is that we find simplifications within L-packets of the two novel invariants introduced in [Kal15], the toral invariant and the admissible L-embedding.