On a classification of irreducible admissible modulo $p$ representations of a $p$-adic split reductive group

TL;DR

This paper classifies irreducible admissible modulo p representations of split p-adic reductive groups using supersingular representations, extending Herzig's theorem to a broader context.

Contribution

It generalizes Herzig's classification theorem to a wider class of split p-adic reductive groups, providing a comprehensive framework for understanding their representations.

Findings

Classification of irreducible admissible modulo p representations

Extension of Herzig's theorem to new group classes

Framework for supersingular representations in this context

Abstract

We give a classification of irreducible admissible modulo $p$ representations of a split $p$-adic reductive group in terms of supersingular representations. This is a generalization of a theorem of Herzig.