Repr\'esentations supercuspidales

TL;DR

This paper reviews methods for constructing supercuspidal representations of p-adic reductive groups, focusing on Bushnell-Kutzko and Yu constructions, and explores their connections through simple characters and Yu data.

Contribution

It provides an overview of two major construction methods and links them via simple characters and Yu data, highlighting their relationship in building supercuspidal representations.

Findings

Bushnell-Kutzko and Yu methods are interconnected.

Simple characters and Yu data are key to understanding these representations.

The paper clarifies the relationship between different construction techniques.

Abstract

This text is a response to the following question: What are the methods to build supercuspidal complex representations of p-adic reductive groups and are there ties between them ? We will give an overview of the Bushnell-Kutzko and Yu constructions. Then, given a simple maximum tame stratum, a simple character $\theta$ associated to this stratum and a representation of the level zero of a subset of G, we associate a Yu data generic and therefore a representation constructed by Yu, this representation corresponds to a simple type given by a $\beta$ - extension of $\theta$.