ON THE EXISTENCE OF ADMISSIBLE SUPERSINGULAR REPRESENTATIONS OF $p$-ADIC REDUCTIVE GROUPS

Abstract

Suppose that $\mathbf{G}$ is a connected reductive group over a finite extension $F/\mathbb{Q}_{p}$ and that $C$ is a field of characteristic $p$. We prove that the group $\mathbf{G}(F)$ admits an irreducible admissible supercuspidal, or equivalently supersingular, representation over $C$.

Keywords

• 22E50
• 11F70
• 20C08