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) (Q1064505)
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scientific article; zbMATH DE number 3919038
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | 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) |
scientific article; zbMATH DE number 3919038 |
Statements
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) (English)
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1984
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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 \textit{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.
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Poisson-Plancherel formula
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Takiff group
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orbital integrals
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Fourier transform
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