Supercuspidal representations in non-defining characteristics

TL;DR

This paper establishes a criterion for supercuspidality of mod-$5$-representations of p-adic groups derived from Yu's construction, linking it to supercuspidal representations of finite reductive groups, without relying on the second adjointness assumption.

Contribution

It proves an if-and-only-if condition for supercuspidality in this context, extending prior results without assuming second adjointness.

Findings

Supercuspidality characterized by originating from finite reductive groups

Extension of previous results without second adjointness assumption

Provides a new criterion for supercuspidal representations

Abstract

We show that a mod-$\ell$-representation of a p-adic group arising from the analogue of Yu's construction is supercuspidal if and only if it arises from a supercuspidal representation of a finite reductive group. This has been previously shown by Henniart and Vigneras under the assumption that the second adjointness holds, a statement that is not yet available in the literature.