Comparison of Bushnell-Kutzko and Yu's constructions of supercuspidal representations

TL;DR

This paper compares two explicit methods for constructing supercuspidal representations of p-adic groups, analyzing their similarities and differences, and discusses the possibility of a unified general construction.

Contribution

It provides a detailed comparison of Bushnell-Kutzko and Yu's constructions, highlighting their relationships and raising questions about a universal approach.

Findings

Explicit comparison of the two constructions

Identification of key similarities and differences

Open question on a general construction

Abstract

We compare precisely and explicitly Bushnell-Kutzko and Yu's constructions of supercuspidal representations. At the end, we draw conclusions and ask a natural question about the existence of a general construction.