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arXiv · 1905.00053

On the existence of admissible supersingular representations of $p$-adic reductive groups

Florian Herzig·Karol Koziol·Marie-France Vignéras
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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 $C$.

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Florian Herzig, Karol Koziol, Marie-France Vignéras. 2019-04-30. On the existence of admissible supersingular representations of $p$-adic reductive groups. https://doi.org/10.1017/fms.2019.50

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