# 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.

## Key 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 $\theta$.

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Source: https://tomesphere.com/paper/1706.05920