The Plancherel formula for complex algebraic unimodular groups
type: Item
instance of: scholarly article
title: The Plancherel formula for complex algebraic unimodular groups
zbMATH Open document ID: 0558.22006
DOI: 10.1007/BF02392819
author: Martin Andler
published in: Acta Mathematica
publication date: 1985-01-01T00:00:00Z
review text: Let \(G\) be a complex algebraic unimodular group, \(\hat G\) its unitary dual. A measure \(\mu\), the Plancherel measure, is given explicitly on \(\hat G,\) so that \(\forall \phi \in C_c^{\infty}(G)\phi (e)=\int_{\hat G}\operatorname{tr}\pi (\phi)\,d\mu (\pi)\). To accomplish this, in the first part of the paper a sufficiently large subset of \(\hat G\) is constructed. Here the main tools are the ''orbit method'', a reduction to the reductive case using Mackey's theory and finally a comparison of the formulas with the known results of Harish Chandra. In the second part the methods developed by M. Duflo for general algebraic groups are adapted to the present case to obtain the Plancherel measure.
reviewed by: Birgit Speh
Mathematics Subject Classification ID: 22E30
zbMATH DE Number: 3889810
zbMATH Keywords: complex algebraic unimodular group
zbMATH Keywords: unitary dual
zbMATH Keywords: Plancherel measure
zbMATH Keywords: orbit method
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3889810