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 $C$.

arXiv comment58 pages, with an appendix by Sug Woo Shin. This replaces arXiv:1712.10142 and arXiv:1808.08255. v2: Minor changes following referee report; to appear in Forum Math. Sigma

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Cited by in corpus (1)

• Restriction of $p$-modular representations of $U(2,1)$ to a Borel subgroup