The Plancherel decomposition for a reductive symmetric space. II. Representation theory

We obtain the Plancherel decomposition for a reductive symmetric space in the sense of representation theory. Our starting point is the Plancherel formula for spherical Schwartz functions, obtained in part I. The formula for Schwartz functions involves Eisenstein integrals obtained by a residual cal...

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Bibliographic Details
Published inInventiones mathematicae Vol. 161; no. 3; pp. 567 - 628
Main Authors van den Ban, E.P., Schlichtkrull, H.
Format Journal Article
LanguageEnglish
Published Heidelberg Springer Nature B.V 01.09.2005
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Summary:We obtain the Plancherel decomposition for a reductive symmetric space in the sense of representation theory. Our starting point is the Plancherel formula for spherical Schwartz functions, obtained in part I. The formula for Schwartz functions involves Eisenstein integrals obtained by a residual calculus. In the present paper we identify these integrals as matrix coefficients of the generalized principal series. [PUBLICATION ABSTRACT]
ISSN:0020-9910
1432-1297
DOI:10.1007/s00222-004-0432-x