Small representations, string instantons, and Fourier modes of Eisenstein series (with an appendix by D. Ciubotaru and P. Trapa)

Understand

This paper concerns some novel features of maximal parabolic Eisenstein series at certain special values of their analytic parameter s.

• These series arise as coefficients in the R4 and D4R4 interactions in the low energy expansion of scattering amplitudes in maximally supersymmetric string theory reduced to D=10-d dimensions on a torus T^d, d<8.
• For each d these amplitudes are automorphic functions on the rank d+1 symmetry group E_d+1.
• Of particular significance is the orbit content of the Fourier modes of these series when expanded in three different parabolic subgroups, corresponding to certain limits of string theory.