Abstract
Let $G$ be a locally compact group and $H$ a closed subgroup of $G$, and let $\pi$ and $\tau$ be irreducible representations of $G$ and $H$, respectively. If $G$ is compact then, by the classical Frobenius reciprocity theorem, $\pi$ is contained in the induced representation ${\rm ind}_H^G \tau$ if and only if $\pi|_H$ contains $\tau$. Topological Frobenius properties, which a general locally compact group may or may not satisfy, are obtained by replacing containment by weak containment of representations. We investigate the `if' and the `only if' assertions for nilpotent locally compact groups and for motion groups.
Original language | English |
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Pages (from-to) | 745-769 |
Number of pages | 25 |
Journal | Journal of Lie Theory |
Volume | 27 |
Issue number | 3 |
Publication status | Published - 31 Dec 2017 |
Keywords
- locally compact group
- nilpotent group
- motion group
- SIN-group
- unitary representation
- induced representation
- weak containment
- topological Frobenius reciprocity
- tensor product