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On the irreducibility of some restrictions in nilpotent Lie groups. (English) Zbl 1442.22008

Summary: Let \(G\) be a connected simply connected nilpotent Lie group and let \(\Gamma\) be a discrete subgroup of \(G\). We characterize the irreducible unitary representations of \(G\) that remain irreducible when restricted to \(\Gamma\).

MSC:

22D05 General properties and structure of locally compact groups
54B20 Hyperspaces in general topology
22E40 Discrete subgroups of Lie groups
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