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A reduction princip...
A reduction principle for Fourier coefficients of automorphic forms
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- Gourevitch, D. (författare)
- Weizmann Institute of Science
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- Gustafsson, Henrik P. A., 1988 (författare)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences,Chalmers tekniska högskola,Chalmers University of Technology,Rutgers University,University of Gothenburg
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- Kleinschmidt, A. (författare)
- Max Planck Gesellschaft zur Förderung der Wissenschaften e.V. (MPG),Max Planck Society for the Advancement of Science (MPG),International Solvay Institute for Physics and Chemistry
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- Persson, Daniel, 1978 (författare)
- Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper,Department of Mathematical Sciences,Chalmers tekniska högskola,Chalmers University of Technology
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- Sahi, S. (författare)
- Rutgers University
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(creator_code:org_t)
- 2021-10-15
- 2022
- Engelska.
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Ingår i: Mathematische Zeitschrift. - : Springer Science and Business Media LLC. - 0025-5874 .- 1432-1823. ; 300, s. 2679-2717
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https://research.cha... (primary) (free)
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https://gup.ub.gu.se...
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https://doi.org/10.1...
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Abstract
Ämnesord
Stäng
- We consider a special class of unipotent periods for automorphic forms on a finite cover of a reductive adelic groupG(AK), which we refer to as Fourier coefficients associated to the data of a 'Whittaker pair'. We describe a quasi-order on Fourier coefficients, and an algorithm that gives an explicit formula for any coefficient in terms of integrals and sums involving higher coefficients. The maximal elements for the quasi-order are 'Levi-distinguished' Fourier coefficients, which correspond to taking the constant term along the unipotent radical of a parabolic subgroup, and then further taking a Fourier coefficient with respect to a K-distinguished nilpotent orbit in the Levi quotient. Thus one can express any Fourier coefficient, including the form itself, in terms of higher Levi-distinguished coefficients. In companion papers we use this result to determine explicit Fourier expansions of minimal and next-to-minimal automorphic forms on split simply-laced reductive groups, and to obtain Euler product decompositions of certain Fourier coefficients.
Ämnesord
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
- NATURVETENSKAP -- Matematik -- Algebra och logik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Algebra and Logic (hsv//eng)
- NATURVETENSKAP -- Matematik -- Geometri (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Geometry (hsv//eng)
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
Nyckelord
- Automorphic function
- Automorphic representation
- Fourier expansion on
- covers of reductive groups
- Whittaker support
- Nilpotent orbit
- Wave-front set
- nilpotent orbits
- representations
- Mathematics
- Automorphic representation
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
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