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

Name: Representations of SU(2,1) in Fourier Term Modules
Brand: Springer Nature
SKU: 9783031431913
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Springer Nature

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9783031431913

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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 Poincar 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 Poincar 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.

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