# Functorial properties of generalised Steinberg representations

Abstract : Let $G$ be the $F$-points of a connected reductive group over a non-archimedean local field $F$ of residue characteristic $p$ and $R$ be a commutative ring. Let $P=LU$ be a parabolic subgroup of $G$ and $Q$ be a parabolic subgroup of $G$ containing $P$. We study the functor $\mathrm{St}_Q^G$ taking a smooth $R$-representation $\sigma$ of $L$ which extends to a representation $\mathrm{e}_G(\sigma)$ of $G$ trivial on $U$ to the smooth $R$-representation $\mathrm{e}_G(\sigma) \otimes_R \mathrm{St}_Q^G(R)$ of $G$ where $\mathrm{St}_Q^G(R)$ is the generalised Steinberg representation.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-01579500
Contributor : Marie-Annick Guillemer <>
Submitted on : Thursday, August 31, 2017 - 11:34:17 AM
Last modification on : Thursday, November 15, 2018 - 11:56:47 AM

### Identifiers

• HAL Id : hal-01579500, version 1
• ARXIV : 1707.06187

### Citation

Julien Hauseux, Tobias Schmidt, Claus Sorensen. Functorial properties of generalised Steinberg representations. 14 pages. 2017. 〈hal-01579500〉

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