The Plancherel decomposition for a reductive symmetric space II. Representation theory
arXiv:math/0111304 · doi:10.1007/s00222-004-0432-x
Abstract
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.
60 pages, LaTeX 2e, revised introduction. Accepted by Invent. Math