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Fourier coefficient...
Fourier coefficients of minimal and next-to-minimal automorphic representations of simply-laced groups
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- Gourevitch, Dmitry (author)
- Weizmann Institute of Science
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- Gustafsson, Henrik, 1988 (author)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences
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- Kleinschmidt, Axel (author)
- Max Planck Institute for Gravitational Physics
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- Persson, Daniel, 1978 (author)
- Chalmers tekniska högskola,Chalmers University of Technology
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- Sahi, Siddhartha (author)
- Rutgers University
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(creator_code:org_t)
- 2022
- 2022
- English.
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In: Canadian Journal of Mathematics. - 1496-4279 .- 0008-414X. ; 74:1, s. 122-169
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Abstract
Subject headings
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- In this paper, we analyze Fourier coefficients of automorphic forms on a finite cover G of an adelic split simply-laced group. Let ππ be a minimal or next-to-minimal automorphic representation of G. We prove that any η∈πη∈π is completely determined by its Whittaker coefficients with respect to (possibly degenerate) characters of the unipotent radical of a fixed Borel subgroup, analogously to the Piatetski-Shapiro–Shalika formula for cusp forms on GLnGLn . We also derive explicit formulas expressing the form, as well as all its maximal parabolic Fourier coefficient, in terms of these Whittaker coefficients. A consequence of our results is the nonexistence of cusp forms in the minimal and next-to-minimal automorphic spectrum. We provide detailed examples for G of type D5D5 and E8E8 with a view toward applications to scattering amplitudes in string theory.
Subject headings
- NATURVETENSKAP -- Matematik -- Algebra och logik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Algebra and Logic (hsv//eng)
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Keyword
- wave-front set
- Automorphic function
- Whittaker support
- minimal representation
- small representations
- nilpotent orbit
- next-to-minimal representation
- string theory
- Whittaker coefficient
- Fourier coefficient
Publication and Content Type
- art (subject category)
- ref (subject category)
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