A short proof of the existence of supercuspidal representations for all reductive $p$-adic groups
Representation Theory
2016-03-09 v2
Abstract
Let be a reductive -adic group. We give a short proof of the fact that 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 .
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}
}