Representations of SU(2,1) in Fourier term modules / Roelof W. Bruggeman, Roberto J. Miatello.

Format:

Book

Author/Creator:

Bruggeman, Roelof W., 1944- Author.

Miatello, Roberto J., Author.

Series:

Lecture notes in mathematics (Springer-Verlag) ; 0075-8434 2340.

Lecture notes in mathematics, 0075-8434 ; 2340

Language:

English

Subjects (All):

Fourier analysis.

Physical Description:

xi, 208 pages : illustrations (black and white, and colour) ; 24 cm.

Place of Publication:

Berlin : Springer, [2023]

Summary:

"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."-- Provided by publisher.

Contents:

1. Introduction

2. The Lie group SU(2,1) and subgroups

3. Fourier term modules

4. Submodule structure

5. Application to automorphic forms.

Notes:

Includes bibliographical references (pages 201-203) and index

ISBN:

303143191X

9783031431913

OCLC:

1391676655