A short proof of the existence of supercuspidal representations for all reductive $p$-adic groups Auteur(s): Beuzart-Plessis Raphaël (Document sans référence bibliographique) 2015-04-01 Ref HAL: hal-01138463_v2 Ref Arxiv: 1504.06157 Ref. & Cit.: NASA ADS Exporter : BibTex | endNote Résumé: Let $G$ be a reductive $p$-adic group. We give a short proof of the fact that $G$ 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 $G$.