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

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...

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Bibliographic Details
Main Authors Henniart, G, Vignéras, M. -F
Format Journal Article
LanguageEnglish
Published 21.12.2017
Subjects
Mathematics - Number Theory
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Summary: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.
DOI:10.48550/arxiv.1712.08038