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 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}
}
Comments
55 pages