Exceptional supercuspidal representations in small residue characteristic

TL;DR

This paper extends the construction of supercuspidal representations in small residue characteristic, producing new examples of higher depth and revealing limitations of existing methods.

Contribution

It introduces new supercuspidal representations in residue characteristic 2 and 3, expanding the known classes and showing some do not originate from Reeder--Yu's construction.

Findings

Constructed new supercuspidal representations of higher depth.

Identified examples not arising from Reeder--Yu's method.

Extended the framework of epipelagic representations in small residue characteristic.

Abstract

In this paper, in residue characteristic 2 and 3, we extend the construction of epipelagic representations of Reeder--Yu to produce new supercuspidals of higher depth, building on work of Gastineau. In particular, we produce examples of epipelagic representations that do not arise from the construction of Reeder--Yu.