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arXiv · 1504.06157

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

Raphaël Beuzart-Plessis
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Abstract

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 $G$.

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BibTeXRIS

Raphaël Beuzart-Plessis. 2015-04-23. A short proof of the existence of supercuspidal representations for all reductive $p$-adic groups. https://doi.org/10.2140/pjm.2016.282.27

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