Growth of homogeneous spaces, density of discrete subgroups and Kazhdan's property \((T)\)
type: Item
instance of: scholarly article
title: Growth of homogeneous spaces, density of discrete subgroups and Kazhdan's property \((T)\)
zbMATH Open document ID: 0787.22011
DOI: 10.1007/BF01232036
author: Garrett Stuck
published in: Inventiones Mathematicae
publication date: 1993-06-29T00:00:00Z
full work available at URL: https://eudml.org/doc/144030
review text: It is shown that if \(G\) is a semisimple Lie group with finite center and no compact factors and if \(H\) is a closed unimodular subgroup of \(G\) such that \(G/H\) has subexponential volume growth, then \(H\) is Zariski dense in \(G\). Moreover, if \(G\) has Kazhdan's property \((T)\) then \(G/H\) must have finite volume. The results are extended to semisimple groups over a local field.
Mathematics Subject Classification ID: 22E15
Mathematics Subject Classification ID: 53C30
zbMATH DE Number: 220746
zbMATH Keywords: growth the homogeneous spaces
zbMATH Keywords: density of discrete subgroups
zbMATH Keywords: semisimple Lie group
zbMATH Keywords: Kazhdan's property (T)
zbMATH Keywords: local field
reviewed by: Kaarin Riives
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 220746