Fourier coefficients attached to small automorphic representations of SL_n(\mathbbA)

2017/07/27 by Ahlén, Olof, Gustafsson, Henrik P. A., Kleinschmidt, Axel +2
#11F30 #11F70 #22E55 #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1707.08937

Abstract

We show that Fourier coefficients of automorphic forms attached to minimal or next-to-minimal automorphic representations of SL_n(\mathbbA) 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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