Modulo p representations of reductive p-adic groups: functorial properties

2017/03/16 by Noriyuki Abe, Guy Henniart, Abe, Noriyuki +3 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT) #primary 20C08 #secondary 11F70

paper · pdf · doi:10.48550/arxiv.1703.05599

openalex publication_date 2017/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let F be a local field with residue characteristic p, let C be an algebraically closed field of characteristic p, and let G be a connected reductive F-group. In a previous paper, Florian Herzig and the authors classified irreducible admissible C-representations of G=G(F) in terms of supercuspidal representations of Levi subgroups of G. Here, for a parabolic subgroup P of G with Levi subgroup M and an irreducible admissible C-representation τ of M, we determine the lattice of subrepresentations of Ind_P^G τ and we show that Ind_P^G χτ is irreducible for a general unramified character χ of M. In the reverse direction, we compute the image by the two adjoints of Ind_P^G of an irreducible admissible representation π of G. On the way, we prove that the right adjoint of Ind_P^G respects admissibility, hence coincides with Emerton's ordinary part functor Ord_P^G on admissible representations.

Citations

• Parabolic induction in characteristic p
• On pro-p-Iwahori invariants of R-representations of reductive p-adic groups

Cited by

• On the Right Derived Functors of Ordinary Parts

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