English

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

Representation Theory 2017-07-28 v1 High Energy Physics - Theory Number Theory

Abstract

We show that Fourier coefficients of automorphic forms attached to minimal or next-to-minimal automorphic representations of SLn(A){\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.

Keywords

Cite

@article{arxiv.1707.08937,
  title  = {Fourier coefficients attached to small automorphic representations of ${\mathrm{SL}}_n(\mathbb{A})$},
  author = {Olof Ahlén and Henrik P. A. Gustafsson and Axel Kleinschmidt and Baiying Liu and Daniel Persson},
  journal= {arXiv preprint arXiv:1707.08937},
  year   = {2017}
}

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55 pages