%0 Unpublished work
%T A short proof of the existence of supercuspidal representations for all reductive $p$-adic groups
%+ Institute for Advanced Study
%A Beuzart-Plessis, RaphaĆ«l
%8 2015-04-01
%D 2015
%Z 1504.06157
%K cusp forms
%K supercuspidal representations
%Z Mathematics [math]/Representation Theory [math.RT]
%Z Mathematics [math]/General Mathematics [math.GM]Preprints, Working Papers, ...
%X 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 $G$.
%G English
%2 https://hal.archives-ouvertes.fr/hal-01138463v2/document
%2 https://hal.archives-ouvertes.fr/hal-01138463/file/existence%20supercuspidal.pdf
%L hal-01138463
%U https://hal.archives-ouvertes.fr/hal-01138463
%~ INSMI