Fourier coefficients attached to small automorphic representations of \(\operatorname{SL}_n(\mathbb{A})\) (Q1786688)

The authors 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. They give an explicit formula for the Fourier expansion, analogously to the Piatetski-Shapiro-Shalika formula. In addition, they derive expressions for Fourier coefficients associated to all maximal parabolic subgroups. These results have possible applications for scattering amplitudes in string theory.