Normalization of intertwining operators and reducibility of representations induced from cuspidal ones; the case of \(p\)-adic classical groups
type: Item
instance of: scholarly article
title: Normalization of intertwining operators and reducibility of representations induced from cuspidal ones; the case of \(p\)-adic classical groups
zbMATH Open document ID: 0956.22012
DOI: 10.2307/121049
published in: Annals of Mathematics. Second Series
publication date: 2000-11-13T00:00:00Z
full work available at URL: 151 2.html
review text: Let \(G(n)\) denote a symplectic or an orthogonal group of rank \(n\) over a non-archimedean local field \(F\). Let \(\pi\) be an irreducible cuspidal representation of \(G(n,F)\) and \(\rho\) an irreducible unitary cuspidal representation of \(\text{GL} (c,F)\). Then \(\text{GL} (c)\times G(n)\) is imbedded in \(G(n+c)\) as a Levi group of a maximal parabolic subgroup and we have the induced representation \(I(\rho,\pi,s) = \rho |\text{det}|^s \times \pi\) of \(\text{GL} (n+c,F)\). The subject of the article is the determination of the values of \(s\) for which this representation is reducible and the normalization of the intertwining operators from \(I(\rho,\pi,s)\) to \(I(\rho^{\ast},\pi,-s)\). A normalization is given under the assumption that \(\pi\) comes from a global representation which satisfies a certain functoriality condition with respect to a general linear group.
Mathematics Subject Classification ID: 22E50
zbMATH DE Number: 1485633
author: Colette Moeglin
reviewed by: J. G. M. Mars
MaRDI profile type: Publication
OpenAlex ID: W4256658331
description: scientific article; zbMATH DE number 1485633