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 nexttominimal 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 PiatetskiShapiroShalika 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:

arXiv eprints
 Pub Date:
 July 2017
 DOI:
 10.48550/arXiv.1707.08937
 arXiv:
 arXiv:1707.08937
 Bibcode:
 2017arXiv170708937A
 Keywords:

 Mathematics  Representation Theory;
 High Energy Physics  Theory;
 Mathematics  Number Theory;
 11F70;
 22E55;
 11F30
 EPrint:
 55 pages