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  Fourier coefficients attached to small automorphic representations of SLn (A)

Ahlen, O., Gustafsson, H. P. A., Kleinschmidt, A., Liu, B., & Persson, D. (2018). Fourier coefficients attached to small automorphic representations of SLn (A). Journal of Number Theory, 192, 80-142. doi:10.1016/j.jnt.2018.03.022.

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Item Permalink: http://hdl.handle.net/11858/00-001M-0000-002D-DB41-2 Version Permalink: http://hdl.handle.net/21.11116/0000-0002-E7BF-3
Genre: Journal Article

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 Creators:
Ahlen, Olof1, Author              
Gustafsson, Henrik P. A., Author
Kleinschmidt, Axel2, Author              
Liu, Baiying, Author
Persson, Daniel, Author
Affiliations:
1Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24014              
2Quantum Gravity and Unified Theories, AEI Golm, MPI for Gravitational Physics, Max Planck Society, ou_24014              

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Free keywords: Mathematics, Representation Theory, math.RT,High Energy Physics - Theory, hep-th,Mathematics, Number Theory, math.NT,
 Abstract: We show that Fourier coefficients of automorphic forms attached to minimal or next-to-minimal automorphic representations of ${\mathrm{SL}}_n(\mathbb{A})$ are completely determined by certain highly degenerate Whittaker coefficients. We give an explicit formula for the Fourier expansion, analogously to the Piatetski-Shapiro-Shalika formula. In addition, we derive expressions for Fourier coefficients associated to all maximal parabolic subgroups. These results have potential applications for scattering amplitudes in string theory.

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 Dates: 2017-07-272017201820182018
 Publication Status: Published in print
 Pages: 55 pages
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 Rev. Method: -
 Identifiers: arXiv: 1707.08937
URI: http://arxiv.org/abs/1707.08937
DOI: 10.1016/j.jnt.2018.03.022
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Title: Journal of Number Theory
Source Genre: Journal
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Pages: - Volume / Issue: 192 Sequence Number: - Start / End Page: 80 - 142 Identifier: -