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Schlagwörter:
High Energy Physics - Theory, hep-th,Mathematics, Number Theory, math.NT,Mathematics, Representation Theory, math.RT
Zusammenfassung:
Motivated by string theory scattering amplitudes that are invariant under a
discrete U-duality, we study Fourier coefficients of Eisenstein series on
Kac-Moody groups. In particular, we analyse the Eisenstein series on E_9(R),
E_10(R) and E_11(R) corresponding to certain degenerate principal series at the
values s=3/2 and s=5/2 that were studied in 1204.3043. We show that these
Eisenstein series have very simple Fourier coefficients as expected for their
role as supersymmetric contributions to the higher derivative couplings R^4 and
\partial^{4} R^4 coming from 1/2-BPS and 1/4-BPS instantons, respectively. This
suggests that there exist minimal and next-to-minimal unipotent automorphic
representations of the associated Kac-Moody groups to which these special
Eisenstein series are attached. We also provide complete explicit expressions
for degenerate Whittaker vectors of minimal Eisenstein series on E_6(R), E_7(R)
and E_8(R) that have not appeared in the literature before.
