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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
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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

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