Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-24T00:25:14.121Z Has data issue: false hasContentIssue false
  • English
  • Français

Ergodic actions on nilmanifolds and restriction of unitary representations to lattices

Published online by Cambridge University Press:  26 October 2001

M. B. BEKKA  and
P. DRIUTTI
M. B. BEKKA
Affiliation:
Université de Metz, Département de Mathématiques, Ile du Saulcy, F-57045 Metz, France
P. DRIUTTI
Affiliation:
Université de Metz, Département de Mathématiques, Ile du Saulcy, F-57045 Metz, France
Get access Rights & Permissions [Opens in a new window]

Abstract

Let G be a nilpotent, connected and simply connected real Lie group and let Γ be a lattice in G. A necessary and sufficient condition is given for a Lie subgroup of G to act ergodically on Γ[setmn ]G. As an application, we characterize the irreducible unitary representations of G for which the restriction to Γ remains irreducible.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 131 , Issue 1 , July 2001 , pp. 91 - 96
Copyright
2001 Cambridge Philosophical Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)