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Ultra-irreducibility of induced representations. (English) Zbl 0706.22004

We prove irreducibility criteria for representations of Lie groups induced from finite dimensional representations of closed subgroups. The representations need not be unitary and the setup allows the representation spaces of the induced representations to be chosen among a variety of different function and distribution spaces. The notion of irreducibility considered is that of ultra-irreducibility which is stronger than complete and topological irreducibility. The criteria are applied to semi-direct products and to nilpotent groups.
Reviewer: J.Jacobsen

MSC:

22D30 Induced representations for locally compact groups
22E27 Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.)
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