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

Raphaël Beuzart-Plessis (1)

1 Institute for Advanced Study

Let $G$ be a reductive $p$-adic group. It can be important for certain global arguments on the trace formula to know that $G$ admits supercuspidal complex representations. We prove that it is always the case. This result has already been established by A. Kret in [K]. Our argument is of a different nature and is based on the Harish-Chandra theory of cusp forms. It ultimately relies on the existence of elliptic maximal tori in $G$.

Mots clés: cusp forms; supercuspidal representations

Domaines: Théorie des représentations [math.RT]; Mathématiques générales [math.GM]

Raphaël Beuzart-Plessis. A short proof of the existence of supercuspidal representations for all reductive $p$-adic groups. 2015. ⟨hal-01138463v1⟩