English

A short proof of the existence of supercuspidal representations for all reductive $p$-adic groups

Representation Theory 2016-03-09 v2

Abstract

Let GG be a reductive pp-adic group. We give a short proof of the fact that GG always admits supercuspidal complex representations. This result has already been established by A. Kret using the Deligne-Lusztig theory of representations of finite groups of Lie type. Our argument is of a different nature and is self-contained. It is based on the Harish-Chandra theory of cusp forms and it ultimately relies on the existence of elliptic maximal tori in GG.

Keywords

Cite

@article{arxiv.1504.06157,
  title  = {A short proof of the existence of supercuspidal representations for all reductive $p$-adic groups},
  author = {Raphaël Beuzart-Plessis},
  journal= {arXiv preprint arXiv:1504.06157},
  year   = {2016}
}