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The Plancherel formula for the horocycle spaces and generalizations, II

Part of: Lie groups

Published online by Cambridge University Press:  09 April 2009

Ronald L. Lipsman
Ronald L. Lipsman
Affiliation:
Department of Mathematics, University of Maryland, College Park, MD 20742USA e-mail: [email protected]
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Abstract

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The Plancherel formula for various semisimple homogeneous spaces with non-reductive stability group is derived within the framework of the Bonnet Plancherel formula for the direct integral decomposition of a quasi-regular representation. These formulas represent a continuation of the author's program to establish a new paradigm for concrete Plancherel analysis on homogeneous spaces wherein the distinction between finite and infinite multiplicity is de-emphasized. One interesting feature of the paper is the computation of the Bonnet nuclear operators corresponding to certain exponential representations (roughly those induced from infinite-dimensional representations of a subgroup). Another feature is a natural realization of the direct integral decomposition over a canonical set of concrete irreducible representations, rather than over the unitary dual.

MSC classification

Secondary: 22E46: Semisimple Lie groups and their representations 22E45: Representations of Lie and linear algebraic groups over real fields
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 65 , Issue 2 , October 1998 , pp. 194 - 211
Copyright
Copyright © Australian Mathematical Society 1998

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