Geodesic
Topological Frobenius Reciprocity for Representations of Nilpotent Groups and Motion Groups
Robert J. Archbold1 ; Eberhard Kaniuth2
1Institute of Mathematics, University of Aberdeen, King's College, Aberdeen AB24 3UE, Scotland, England
2Institut für Mathematik, Universität Paderborn, 33095 Paderborn, Germany
Journal of Lie Theory, Tome 27 (2017) no. 3, pp. 745-769

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Classification : 22D10, 22D30
Mots-clés : Locally compact group, nilpotent group, motion group, SIN-group, unitary representation, induced representation, weak containment, topological Frobenius reciprocity, tensor product

Robert J. Archbold  1   ; Eberhard Kaniuth  2

1 Institute of Mathematics, University of Aberdeen, King's College, Aberdeen AB24 3UE, Scotland, England
2 Institut für Mathematik, Universität Paderborn, 33095 Paderborn, Germany 
Robert J. Archbold; Eberhard Kaniuth. Topological Frobenius Reciprocity for Representations of Nilpotent Groups and Motion Groups. Journal of Lie Theory, Tome 27 (2017) no. 3, pp. 745-769. http://geodesic.mathdoc.fr/item/JOLT_2017_27_3_a6/
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     author = {Robert J. Archbold and Eberhard Kaniuth},
     title = {Topological {Frobenius} {Reciprocity} for {Representations} of {Nilpotent} {Groups} and {Motion} {Groups}},
     journal = {Journal of Lie Theory},
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