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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Type de document :
Pré-publication, Document de travail
14 pages. 2017
Domaine :

https://hal.archives-ouvertes.fr/hal-01579500
Contributeur : Marie-Annick Guillemer <>
Soumis le : jeudi 31 août 2017 - 11:34:17
Dernière modification le : mercredi 18 octobre 2017 - 14:38:05

Identifiants

• 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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