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.

14 pages, minor changes, final version

References in corpus (5)

• A classification of irreducible admissible mod p representations of p-adic reductive groups
• On special representations of $p$-adic reductive groups
• Parabolic induction and extensions
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Cited by in corpus (3)

• p-adic etale cohomology of period domains
• Deformation rings and parabolic induction
• From $p$-modular to $p$-adic Langlands correspondences for $U(1,1)({\mathbb{Q}}_{p^2}/{\mathbb{Q}}_p)$: deformations in the non-supercuspidal case