Representations of SU(2,1) in fourier term modules

• Verfasst von: Bruggeman, Roelof W. [VerfasserIn]
• Verfasst von: Miatello, Roberto J. [VerfasserIn]
• Titel: Representations of SU(2,1) in fourier term modules
• Verf.angabe: Roelof W. Bruggeman, Roberto J. Miatello
• Verlagsort: Cham
• Verlag: Springer
• Jahr: 2023
• Umfang: 1 Online-Ressource (XI, 210 Seiten)
• Gesamttitel/Reihe: Lecture notes in mathematics ; volume 2340
• ISBN: 978-3-031-43192-0
• DOI: doi:10.1007/978-3-031-43192-0
• Schlagwörter: (s)Automorphe Form / (s)Automorphe Darstellung / (s)Halbeinfache Lie-Gruppe / (s)Fourier-Entwicklung / (s)Untermodul / (s)Poincaré-Reihe
• Datenträger: Online-Ressource
• Sprache: eng
• Bibliogr. Hinweis: Erscheint auch als : Druck-Ausgabe: Bruggeman, Roelof W., 1944 - : Representations of SU(2,1) in fourier term modules. - Cham : Springer, 2023. - xi, 208 Seiten
• K10plus-PPN: 1870463889
• K10plus-PPN:
  Universitätsbibliothek
• Lokale URL UB: Zum Volltext

Abstract

This book studies the modules arising in Fourier expansions of automorphic forms, namely Fourier term modules on SU(2,1), the smallest rank one Lie group with a non-abelian unipotent subgroup. It considers the “abelian” Fourier term modules connected to characters of the maximal unipotent subgroups of SU(2,1), and also the “non-abelian” modules, described via theta functions. A complete description of the submodule structure of all Fourier term modules is given, with a discussion of the consequences for Fourier expansions of automorphic forms, automorphic forms with exponential growth included. These results can be applied to prove a completeness result for Poincaré series in spaces of square integrable automorphic forms. Aimed at researchers and graduate students interested in automorphic forms, harmonic analysis on Lie groups, and number-theoretic topics related to Poincaré series, the book will also serve as a basic reference on spectral expansion with Fourier-Jacobi coefficients. Only a background in Lie groups and their representations is assumed.