On reducibility of parabolic induction
type: Item
instance of: scholarly article
title: On reducibility of parabolic induction
zbMATH Open document ID: 0914.22019
DOI: 10.1007/BF02764004
author: Marko Tadić
published in: Israel Journal of Mathematics
publication date: 1999-06-14T00:00:00Z
review text: The subject of the paper is the investigation of reducibility of parabolically induced representations of \(\text{Sp}(2n,F)\) and \(\text{SO}(2n+1,F)\), where \(F\) is a non-archimedean local field, by applying parabolic restriction to these representations. There is a variety of general results in which reducibility of induced representations is related to reducibility of representations induced from cuspidal representations. From given concrete applications I mention the determination of the composition series for representations induced from a one-dimensional representation of certain maximal parabolic subgroups. The method of this paper was used later by C. Jantzen to complete the determination of the composition series of representations induced from a one-dimensional representation of an arbitrary parabolic subgroup.
Mathematics Subject Classification ID: 22E50
zbMATH DE Number: 1239659
zbMATH Keywords: reducibility
zbMATH Keywords: parabolically induced representations
zbMATH Keywords: parabolic subgroups
zbMATH Keywords: composition series
reviewed by: J. G. M. Mars
MaRDI profile type: Publication
cites work: Self-contragredient supercuspidal representations of $\mathrm {GL}_n$
cites work: Dualite Dans Le Groupe De Grothendieck De La Categorie Des Representations Lisses De Longueur Finie D'un Groupe Reductif p-Adique
cites work: Induced representations of reductive ${\germ p}$-adic groups. I
cites work: Q4777531
cites work: L-indistinguishability and R groups for the special linear group
cites work: Reducibility of Induced Representations for SP(2N) and SO(N)
cites work: The degenerate principal series for 𝑆𝑝(2𝑛)
cites work: Degenerate principal series for symplectic groups
cites work: Degenerate principal series for orthogonal groups.
cites work: Degenerate principal series for symplectic and odd-orthogonal groups
cites work: Q5687449
cites work: Ramified degenerate principal series representations for \(Sp(n)\)
cites work: Howe correspondences on a \(p\)-adic field
cites work: Q4214809
cites work: Q4228080
cites work: Whittaker models and unipotent representations of \(p\)-adic groups
cites work: Hecke algebras and harmonic analysis on p -adic groups
cites work: Q3916765
cites work: Q4743014
cites work: Sur les représentations non ramifiées des groupes réductifs $p$-adiques ; l'exemple de $GSp(4)$
cites work: Representation theory and sheaves on the Bruhat-Tits building
cites work: Induced representations and classification for $GSp(2,F)$ and $Sp(2,F)$
cites work: A proof of Langlands' conjecture on Plancherel measures; complementary series for \(p\)-adic groups
cites work: Twisted endoscopy and reducibility of induced representations for \(p\)- adic groups
cites work: Discrete Series and Classification for p-Adic Groups I
cites work: Classification of unitary representations in irreducible representations of general linear group (non-Archimedean case)
cites work: Induced representations of GL (n, A) for p-adic division algebras A.
cites work: Notes on representation theory of non-Archimedean \(SL(n)\)
cites work: Q4012132
cites work: Q4286083
cites work: Structure arising from induction and Jacquet modules of representations of classical \(p\)-adic groups
cites work: On regular square integrable representations of p -adic groups
cites work: Un exercice sur $GSp(4,F)$ et les représentations de Weil
cites work: Induced representations of reductive ${\germ p}$-adic groups. II. On irreducible representations of ${\rm GL}(n)$
description: scientific article; zbMATH DE number 1239659