✦ LIBER ✦

Moyal Product and Representations of Solvable Lie Groups

✍ Scribed by D Arnal; J.C Cortet; J Ludwig

Publisher: Elsevier Science
Year: 1995
Tongue: English
Weight: 640 KB
Volume: 133
Category: Article
ISSN: 0022-1236
DOI: 10.1006/jfan.1995.1131

No coin nor oath required. For personal study only.

✦ Synopsis

Using a parametrization for the universal covering (c_{10}) of any coadjoint orbit (c) of a solvable (connected and simply connected) Lie group (G), we prove that the Moyal product on (\mathfrak{c}{0}) gives a realization of the unitary representations canonically associated to the orbit ( in Pukanszky's theory by deformation of the algebra of (C^{4}) functions on (\left({0}\right.). By restriction to the standard covering ((\hat{C}), we describe a structure of algebra on (L^{2}(\hat{C})) and an adapted Fourier transform for type (I) group (G). iv 1995 Academic Press, Inc.

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