Unitary spectrum and the fundamental group for actions of semisimple Lie groups
type: Item
instance of: scholarly article
title: Unitary spectrum and the fundamental group for actions of semisimple Lie groups
zbMATH Open document ID: 0681.22014
DOI: 10.1007/BF01446923
author: Robert J. Zimmer
published in: Mathematische Annalen
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164715
review text: We discuss conditions on a smooth action of a semisimple Lie group that imply the existence of a large discrete spectral component in the induced representation on the space of square integrable functions. In particular, we exhibit the basic role played by the fundamental group of the manifold for the existence of discrete spectrum.
Mathematics Subject Classification ID: 22E46
Mathematics Subject Classification ID: 57S25
Mathematics Subject Classification ID: 53C10
zbMATH DE Number: 4114915
zbMATH Keywords: smooth action
zbMATH Keywords: semisimple Lie group
zbMATH Keywords: large discrete spectral component
zbMATH Keywords: induced representation
zbMATH Keywords: square integrable functions
zbMATH Keywords: fundamental group
Wikidata QID: Q115393511
MaRDI profile type: Publication
cites work: Q3687381
cites work: Representations of Fundamental Groups of Manifolds with a Semisimple Transformation Group
cites work: Volume preserving actions of lattices in semisimple groups on compact manifolds
cites work: Infinitesimal regidity for smooth actions of discrete subgroups of Lie groups
description: scientific article; zbMATH DE number 4114915