Fourier coefficients attached to small automorphic representations of ${\mathrm{SL}}_n(\mathbb{A})$
Abstract
We show that Fourier coefficients of automorphic forms attached to minimal or next-to-minimal automorphic representations of ${\mathrm{SL}}_n(\mathbb{A})$ are completely determined by certain highly degenerate Whittaker coefficients. We give an explicit formula for the Fourier expansion, analogously to the Piatetski-Shapiro-Shalika formula. In addition, we derive expressions for Fourier coefficients associated to all maximal parabolic subgroups. These results have potential applications for scattering amplitudes in string theory.
- Publication:
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arXiv e-prints
- Pub Date:
- July 2017
- DOI:
- 10.48550/arXiv.1707.08937
- arXiv:
- arXiv:1707.08937
- Bibcode:
- 2017arXiv170708937A
- Keywords:
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- Mathematics - Representation Theory;
- High Energy Physics - Theory;
- Mathematics - Number Theory;
- 11F70;
- 22E55;
- 11F30
- E-Print:
- 55 pages