Fourier coefficients attached to small automorphic representations of SLn (A)
Journal article, 2018

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

Scattering amplitudes

Nilpotent orbits

Fourier coefficients

Fourier expansion

Small automorphic forms

String Theory


Olof Ahlen

Max Planck Society

Henrik Gustafsson

Chalmers, Physics, Theoretical Physics

Axel Kleinschmidt

Université libre de Bruxelles (ULB)

Max Planck Society

Baiying Liu

Purdue University

Daniel Persson

Chalmers, Mathematical Sciences, Algebra and geometry

Journal of Number Theory

0022-314X (ISSN) 1096-1658 (eISSN)

Vol. 192 80-142

Subject Categories

Algebra and Logic


Mathematical Analysis



More information

Latest update