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We show that Fourier coefficients of automorphic forms attached to minimal ornext-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 thePiatetski-Shapiro-Shalika formula. In addition, we derive expressions forFourier coefficients associated to all maximal parabolic subgroups. Theseresults have potential applications for scattering amplitudes in string theory.

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