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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Disintegrating tensor representations of nilpotent Lie groups

Authors: Jawhar Abdennadher and Jean Ludwig
Journal: Trans. Amer. Math. Soc. 361 (2009), 819-848
MSC (2000): Primary 22E27
Published electronically: September 29, 2008
MathSciNet review: 2452826
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Abstract: Let $ G$ be a simply connected nilpotent Lie group and $ H$ a closed connected subgroup of $ G$. Given an irreducible unitary representation $ \pi$ of $ G$, we present an explicit disintegration of the restriction $ \pi_{\vert H}$ of $ \pi$ to $ H$. Such a disintegration relies on the description of the double cosets space $ H \diagdown G\diagup B$ for an arbitrary closed connected subgroup $ B$ of $ G$, and the well-known smooth disintegration of monomial representations of nilpotent Lie groups. As an application we get a concrete disintegration and a criterion of irreducibility for tensor products of a finite number of irreducible representations of $ G$.

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Additional Information

Jawhar Abdennadher
Affiliation: Département de Mathématiques, Faculté des Sciences de Sfax, RTE de Soukra KM 4. B. P. 802, 3018, Sfax, Tunisia

Jean Ludwig
Affiliation: Département de Mathématiques, Laboratoire LMAM UMR 7122, Université de Metz, Ile du Saulcy, F-57045 Metz Cedex 1, France

Received by editor(s): March 16, 2007
Published electronically: September 29, 2008
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.