Representations of the unitary group SU(2,1) in Fourier term modules
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arXiv
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| Format: | Preprint |
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2019
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| _version_ | 1866911758978908160 |
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| author | Bruggeman, Roelof W. Miatello, Roberto J. |
| author_facet | Bruggeman, Roelof W. Miatello, Roberto J. |
| contents | We study Fourier term modules on $\mathrm{SU}(2,1)$, which are the modules arising in Fourier expansions of automorphic forms. Maximal unipotent subgroups $N$ of $\mathrm{SU}(2,1)$ are non-abelian, and we consider the ``abelian'' Fourier term modules connected to characters of $N$, and also the ``non-abelian'' modules described with theta functions. Poincaré series for $\mathrm{SU}(2,1)$ have in general exponential growth. To deal with such generalized automorphic forms we allow exponential growth for the functions in Fourier term modules. We give a complete description of the submodule structure of all Fourier term modules, and discuss the consequences for Fourier expansions of automorphic forms. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_1912_01334 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Representations of the unitary group SU(2,1) in Fourier term modules Bruggeman, Roelof W. Miatello, Roberto J. Representation Theory 11F70, 11F55, 22E30 We study Fourier term modules on $\mathrm{SU}(2,1)$, which are the modules arising in Fourier expansions of automorphic forms. Maximal unipotent subgroups $N$ of $\mathrm{SU}(2,1)$ are non-abelian, and we consider the ``abelian'' Fourier term modules connected to characters of $N$, and also the ``non-abelian'' modules described with theta functions. Poincaré series for $\mathrm{SU}(2,1)$ have in general exponential growth. To deal with such generalized automorphic forms we allow exponential growth for the functions in Fourier term modules. We give a complete description of the submodule structure of all Fourier term modules, and discuss the consequences for Fourier expansions of automorphic forms. |
| title | Representations of the unitary group SU(2,1) in Fourier term modules |
| topic | Representation Theory 11F70, 11F55, 22E30 |
| url | https://arxiv.org/abs/1912.01334 |