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
Author
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 80-142Subject Categories
Algebra and Logic
Geometry
Mathematical Analysis
DOI
10.1016/j.jnt.2018.03.022