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# Fourier expansions of Kac-Moody Eisenstein series and degenerate Whittaker vectors

Philipp Fleig ; Axel Kleinschmidt ; Daniel Persson (Institutionen för fundamental fysik)
Communications in Number Theory and Physics (1931-4523). Vol. 8 (2014), 1, p. 41-100.

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.

Submitted for publication in CNTP

CPL Pubid: 192464

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# Institutioner (Chalmers)

Institutionen för fundamental fysik (2005-2015)