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Fourier expansions ...
Fourier expansions of Kac-Moody Eisenstein series and degenerate Whittaker vectors
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Fleig, Philipp (author)
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Kleinschmidt, Axel (author)
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- Persson, Daniel, 1978 (author)
- Chalmers tekniska högskola,Chalmers University of Technology
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(creator_code:org_t)
- 2014
- 2014
- English.
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In: Communications in Number Theory and Physics. - 1931-4531 .- 1931-4523. ; 8:1, s. 41-100
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http://dx.doi.org/10...
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Abstract
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- 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.
Subject headings
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
- NATURVETENSKAP -- Fysik -- Annan fysik (hsv//swe)
- NATURAL SCIENCES -- Physical Sciences -- Other Physics Topics (hsv//eng)
- NATURVETENSKAP -- Matematik -- Diskret matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Discrete Mathematics (hsv//eng)
Publication and Content Type
- art (subject category)
- ref (subject category)
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