Up-down representations and ergodic theory in nilpotent Lie groups
type: Item
instance of: scholarly article
title: Up-down representations and ergodic theory in nilpotent Lie groups
zbMATH Open document ID: 1171.22004
author: Hatem Hamrouni
published in: Manuscripta Mathematica
publication date: 2009-02-26T00:00:00Z
review text: This paper gives a new necessary and sufficient condition for a nilflow \((G/\Gamma,A)\) to be ergodic where \(G\) is a simply connected nilpotent Lie group and \(\Gamma\) is a lattice subgroup of \(G\). \(A\) is a connected one-parameter subgroup of \(G\). The results are simpler than similar results previously obtained by Auslander, Green and Hahn. The author gives an explicit decomposition into irreducibles of the up-down representation \((\text{Ind}^G_\Gamma 1)_A\).
reviewed by: Meera G. Mainkar
Mathematics Subject Classification ID: 22E25
Mathematics Subject Classification ID: 22E27
Mathematics Subject Classification ID: 22D40
zbMATH DE Number: 5520093
zbMATH Keywords: nilpotent Lie group
zbMATH Keywords: nilflow
zbMATH Keywords: up-down representation
MaRDI profile type: Publication
Wikidata QID: Q115388381
full work available at URL: s00229-008-0212-9
OpenAlex ID: W2079691734
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DOI: 10.1007/S00229-008-0212-9
description: scientific article; zbMATH DE number 5520093