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

Axel Kleinschmidt; Baiying Liu; Daniel Persson; Henrik P. A. Gustafsson; Olof Ahl\'en

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

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arxiv 1707.08937 v1 pith:AEHNXNOK submitted 2017-07-27 math.RT hep-thmath.NT

Olof Ahlén , Henrik P. A. Gustafsson , Axel Kleinschmidt , Baiying Liu , Daniel Persson This is my paper · ORCID

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keywords coefficientsfourierautomorphicattachedformulamathbbmathrmrepresentations

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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.

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Fourier coefficients of minimal and next-to-minimal automorphic representations of simply-laced groups
math.NT 2019-08 conditional novelty 7.0 of 10

Minimal and next-to-minimal automorphic functions on split simply-laced groups are uniquely determined by, and explicitly reconstructible from, their Whittaker coefficients.

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