Composition series of generalized principal series; the case of strongly positive discrete series
type: Item
instance of: scholarly article
title: Composition series of generalized principal series; the case of strongly positive discrete series
zbMATH Open document ID: 1055.22015
DOI: 10.1007/BF02786631
author: Goran Muić
published in: Israel Journal of Mathematics
publication date: 2004-11-11T00:00:00Z
review text: This paper is devoted to the study of the structure of certain representations of either the symplectic groups or full orthogonal groups over a \(p\)-adic field, \(F\). Let \(R(G)\) denote the Grothendieck group of representations of finite length of groups in the tower; let \(R(GL)\) be the Grothendieck group of representations of finite length of a general linear group. There is a natural map, due to Tadić, from \(R(G)\) to \(R(G) \otimes R(GL(n))\). This arises as the maximal parabolic subgroup of the group \(G_n\) of split rank \(n\) in the tower has Levi component \(GL(j,F) \times G_{n-j}\). The purpose of this paper is to determine the composition series of induction from a parabolic subgroup, the representation on the \(G_n\) factor is a strongly positive discrete series representation. The representations of the general linear groups are relatively well understood. The final results are complete but too intricate to be summarized here.
Mathematics Subject Classification ID: 22E50
zbMATH DE Number: 2114398
zbMATH Keywords: representation theory
zbMATH Keywords: local fields
zbMATH Keywords: composition series
zbMATH Keywords: Langlands parameters
zbMATH Keywords: principal series
zbMATH Keywords: series
zbMATH Keywords: orthogonal group
zbMATH Keywords: symplectic group
reviewed by: Samuel James Patterson
MaRDI profile type: Publication
cites work: Degenerate principal series for symplectic and odd-orthogonal groups
cites work: Q4214809
cites work: A proof of Casselman-Shahidi's conjecture for quasi-split classical groups
cites work: Howe correspondence for discrete series representations; the case of (Sp(n);O(V))
cites work: Reducibility of Generalized Principal Series
cites work: Q1614961
cites work: Construction of discrete series for classical 𝑝-adic groups
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: On reducibility of parabolic induction
cites work: LA FORMULE DE PLANCHEREL POUR LES GROUPES p-ADIQUES. DAPRS HARISH-CHANDRA
cites work: Induced representations of reductive ${\germ p}$-adic groups. II. On irreducible representations of ${\rm GL}(n)$
full work available at URL: https://doi.org/10.1007/bf02786631
OpenAlex ID: W2089663189
description: scientific article; zbMATH DE number 2114398