Cambridge Journal of Mathematics

Volume 10 (2022)

Number 3

A Paley–Wiener theorem for Harish–Chandra modules

Pages: 689 – 742

DOI: https://dx.doi.org/10.4310/CJM.2022.v10.n3.a3

Authors

Heiko Gimperlein (Engineering Mathematics , Leopold-Franzens-Universität Innsbruck, Austria)

Bernhard Krötz (Institute für Mathematik, Universität Paderborn, Germany)

Job Kuit (Institute für Mathematik, Universität Paderborn, Germany)

Henrik Schlichtkrull (Department of Mathematical Sciences, University of Copenhagen, Denmark)

Abstract

We formulate and prove a Paley–Wiener theorem for Harish–Chandra modules for a real reductive group. As a corollary we obtain a new and elementary proof of the Helgason conjecture.

Keywords

minimal globalization, Helgason conjecture

2010 Mathematics Subject Classification

Primary 22E45. Secondary 43A85.

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Received 9 January 2021

Published 22 July 2022