Representations of SU(2,1) in Fourier Term Modules (Lecture Notes in Mathematics 2340) （1st ed. 2023. 2023. xi, 210 S. XI, 210 p. 66 illus., 51 illus. in colo）

Bruggeman, Roelof W./Miatello, Roberto J.

SPRINGER, BERLIN; SPRINGER NATURE SWITZERLAND; SPRING（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.

Contents

- 1. Introduction. - 2. The Lie Group SU(2,1) and Subgroups. - 3. Fourier Term Modules. - 4. Submodule Structure. - 5. Application to Automorphic Forms.