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

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

2001-11-29

arxiv.org/abs/math/0111304v4

Inventiones Mathematicae 161 (3) 2005, 567 - 628

Mathematics

Representation Theory

60 pages, LaTeX 2e, revised introduction. Accepted by Invent. Math

Scientific paper

10.1007/s00222-004-0432-x

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 (math.RT/0107063). 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.

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