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Induced Representations of Locally Compact Groups by Keith F. Taylor, Eberhard Kaniuth

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6

Topological Frobenius properties

Let G be a locally compact group and H a closed subgroup of G, and suppose that π and τ are irreducible representations of G and H, respectively. If G is compact, then according to the classical Frobenius reciprocity theorem, the restriction π|H contains τ as a subrepresentation if and only if π is contained in the induced representation images. In Section 2.9 we have presented a somewhat more general result, but also indicated limitations of further extensions. Such severe limitations led to the replacement of containment of representations by weak containment and the subsequent development of a rich and nuanced ...

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