Titel
On the notion of the parabolic and the cuspidal support of smooth-automorphic forms and smooth-automorphic representations
Autor*in
Sonja Žunar
University of Zagreb Faculty of Geodesy
Abstract
In this paper we describe several new aspects of the foundations of the representation theory of the space of smooth-automorphic forms (i.e., not necessarily K∞-finite automorphic forms) for general connected reductive groups over number fields. Our role model for this space of smooth-automorphic forms is a “smooth version” of the space of automorphic forms, whose internal structure was the topic of Franke’s famous paper (Ann Sci de l’ENS 2:181–279, 1998). We prove that the important decomposition along the parabolic support, and the even finer—and structurally more important—decomposition along the cuspidal support of automorphic forms transfer in a topologized version to the larger setting of smooth-automorphic forms. In this way, we establish smooth-automorphic versions of the main results of Franke and Schwermer (Math Ann 311:765–790, 1998) and of Mœglin and Waldspurger (Spectral Decomposition and Eisenstein Series, Cambridge University Press, 1995), III.2.6.
Stichwort
Automorphic formAutomorphic representationSmooth-automorphic representationCuspidalParabolic supportCuspidal support
Objekt-Typ
Sprache
Englisch [eng]
Persistent identifier
phaidra.univie.ac.at/o:2068203
Erschienen in
Titel
Monatshefte für Mathematik
ISSN
0026-9255
Erscheinungsdatum
2024
Publication
Springer Science and Business Media LLC
Erscheinungsdatum
2024
Zugänglichkeit
Rechteangabe
© The Author(s) 2024

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