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Sur les restrictions des représentations unitaires des groupes de Lie résolubles exponentiels. (On the restrictions of unitary representations of exponential solvable Lie groups). (French) Zbl 0702.22012
Let G be an exponential solvable Lie group, \(\pi\) an irreducible unitary representation of G, and let K be an analytic subgroup of G. We describe the canonical central decomposition of the restriction of \(\pi\) to K. This is done by the orbit method due to Kirillov. As corollary, we observe a Frobenius reciprocity and get the irreducible decomposition of the tensor product of unitary representations. These results were first shown by Corwin and Greenleaf in nilpotent case, then by Lipsman in completely solvable case.
Reviewer: H.Fujiwara

MSC:
22E27 Representations of nilpotent and solvable Lie groups (special orbital integrals, non-type I representations, etc.)
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References:
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