Representations of SU(2,1) in Fourier Term Modules (Lecture Notes in Mathematics)

Bruggeman, Roelof W./ Miatello, Roberto J.

Springer, Berlin; Springer（2023発売）

Springer, Berlin; Springer（2023発売）

• 製本 Paperback:紙装版/ペーパーバック版
• 商品コード 9783031431913

Full Description

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.