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Ergodic actions on nilmanifolds and restriction of unitary representations to lattices
Published online by Cambridge University Press: 26 October 2001
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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