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

Fleig, P., Kleinschmidt, A., & Persson, D. (2014). Fourier expansions of Kac-Moody Eisenstein series and degenerate Whittaker vectors. Communications in Number Theory and Physics, 8(1), 41-100. doi:10.4310/CNTP.2014.v8.n1.a2.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-0014-D1B4-8 Version Permalink: http://hdl.handle.net/11858/00-001M-0000-0024-3B11-A
Genre: Journal Article

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1312.3643.pdf (Preprint), 589KB
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 Creators:
Fleig, Philipp1, Author              
Kleinschmidt, Axel2, Author              
Persson, Daniel, Author
Affiliations:
1Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, Golm, DE, escidoc:24014              
2Quantum Gravity and Unified Theories, AEI Golm, MPI for Gravitational Physics, Max Planck Society, escidoc:24014              

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Free keywords: High Energy Physics - Theory, hep-th,Mathematics, Number Theory, math.NT,Mathematics, Representation Theory, math.RT
 Abstract: 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.

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 Dates: 2013-12-122014
 Publication Status: Published in print
 Pages: 60 pages
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 Rev. Method: -
 Identifiers: arXiv: 1312.3643
DOI: 10.4310/CNTP.2014.v8.n1.a2
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Title: Communications in Number Theory and Physics
Source Genre: Journal
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Pages: - Volume / Issue: 8 (1) Sequence Number: - Start / End Page: 41 - 100 Identifier: -