The Second Adjointness Theorem for reductive p-adic groups

2010/04/24 by Ralf Meyer, Maarten Solleveld, Meyer, Ralf +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1004.4290

openalex publication_date 2010/04/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the Jacquet restriction functor for a parabolic subgroup of a reductive group over a non-Archimedean local field is right adjoint to the parabolic induction functor for the opposite parabolic subgroup, in the generality of smooth group representations on R-modules for any unital ring R in which the residue field characteristic is invertible. Correction: it turned out that the paper contains a mistake (in Lemma 3.4), which the authors have been unable to fix. This renders the proof of the main theorem incomplete.

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