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La formule de Poisson-Plancherel pour un groupe de Takiff associé à un groupe de Lie semi-simple à centre fini. (The Poisson-Plancherel formula for a Takiff group associated to a semi-simple Lie group with finite centre). (French) Zbl 0575.43005
The semi-direct product of a semi-simple Lie group with finite centre by its Lie algebra is called a Takiff group. This paper establishes the Plancherel formula for such a group, as conjectured by M. Vergne [cf. Ann. Math., II. Ser. 115, 639-666 (1982; Zbl 0501.43006)]. The main technical problem is to define an analogue of orbital integrals which makes sense at singular points, and to calculate its Fourier transform.
Reviewer: J.Repka

MSC:
43A80 Analysis on other specific Lie groups
22E46 Semisimple Lie groups and their representations
22E30 Analysis on real and complex Lie groups
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