Representations of a $p$-adic group in characteristic $p$

G. Henniart; M. -F. Vignéras

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arXiv · 1712.08038

Representations of a $p$-adic group in characteristic $p$

G. Henniart·M. -F. Vignéras

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Abstract

Let $F$ be a locally compact non-archimedean field of residue characteristic $p$, $\textbf{G}$ a connected reductive group over $F$, and $R$ a field of characteristic $p$. When $R$ is algebraically closed, the irreducible admissible $R$-representations of $G=\textbf{G}(F)$ are classified in term of supersingular $R$-representations of the Levi subgroups of $G$ and parabolic induction; there is a similar classification for the simple modules of the pro-$p$ Iwahori Hecke $R$-algebra. In this paper, we show that both classifications hold true when $R$ is not algebraically closed.

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G. Henniart, M. -F. Vignéras. 2017-12-21. Representations of a $p$-adic group in characteristic $p$. https://arxiv.org/abs/1712.08038

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