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Analyse conforme sur les algèbres de Jordan

Part of: Harmonic analysis in several variables Jordan algebras

Published online by Cambridge University Press:  09 April 2009

M. Pevzner
M. Pevzner
Affiliation:
Université Libre de Bruxelles, CP 218, Campus de la Plaine, 1050 Brussels, Belgium e-mail: mpevzner@ulb.ac.be
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Abstract

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We construct the Weil representation of the Kantor-Koecher-Tits Lie algebra g associated to a simple real Jordan algebra V. Later we introduce a family of integral operators intertwining the Weil representation with the infinitesimal representations of the degenerate principal series of the conformal group G of the Jordan algebra V. The decomposition of L2(V) in the case of Jordan algebra of real square matrices is given using this construction.

MSC classification

Secondary: 42B35: Function spaces arising in harmonic analysis 17C30: Associated groups, automorphisms
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 73 , Issue 2 , October 2002 , pp. 279 - 300
Copyright
Copyright © Australian Mathematical Society 2002

References

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