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

• 成果类型: Article
• 署名作者: van den Ban, EP; Schlichtkrull, H
• 署名单位: Utrecht University; Aarhus University; University of Copenhagen
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-004-0432-x
• 发表日期: 2005
• 页码: 567-628
• 关键词: invariant distribution vectors; generalized principal series; eisenstein integrals; Operators; FORMULA

摘要

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.