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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.
We provide an explicit set of algebraically independent generators for the algebra of invariant differential operators on the Riemannian symmetric space associated with $SL_n(R)$.
In this paper we analyze Fourier coefficients of automorphic forms on a finite cover $G$ of an adelic split simply-laced group. Let $pi$ be a minimal or next-to-minimal automorphic representation of $G$. We prove that any $etain pi$ is completely det
We study the question of Eulerianity (factorizability) for Fourier coefficients of automorphic forms, and we prove a general transfer theorem that allows one to deduce the Eulerianity of certain coefficients from that of another coefficient. We also
We consider a general class of Fourier coefficients for an automorphic form on a finite cover of a reductive adelic group ${bf G}(mathbb{A}_{mathbb{K}})$, associated to the data of a `Whittaker pair. We describe a quasi-order on Fourier coefficients,
In this paper, we study top Fourier coefficients of certain automorphic representations of $mathrm{GL}_n(mathbb{A})$. In particular, we prove a conjecture of Jiang on top Fourier coefficients of isobaric automorphic representations of $mathrm{GL}_n(m