Fourier coefficients of minimal and next-to-minimal automorphic representations of simply-laced groups

DOI10.4153/S0008414X20000711zbMath1489.11065arXiv1908.08296OpenAlexW3088336766MaRDI QIDQ5029490

Axel Kleinschmidt, Dmitry Gourevitch, Henrik P. A. Gustafsson, Daniel Persson, Siddhartha Sahi

Publication date: 14 February 2022

Published in: Canadian Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1908.08296

zbMATH Keywords

string theoryminimal representationnilpotent orbitFourier coefficientwave-front setsmall representationsWhittaker coefficientautomorphic functionWhittaker supportnext-to-minimal representation

Mathematics Subject Classification ID

Fourier coefficients of automorphic forms (11F30) Representation-theoretic methods; automorphic representations over local and global fields (11F70) Applications of linear algebraic groups to the sciences (20G45) Representations of Lie and linear algebraic groups over global fields and adèle rings (22E55)

Related Items (3)

Saturating unitarity bounds at U-duality symmetric points ⋮ Perturbative higher-derivative terms in \(\mathcal{N} = 6\) asymmetric orbifolds ⋮ A reduction principle for Fourier coefficients of automorphic forms

Cites Work

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• Small automorphic representations and degenerate Whittaker vectors
• \(R^4\) couplings and automorphic unipotent representations
• Fourier coefficients of automorphic forms, character variety orbits, and small representations
• Small representations, string instantons, and Fourier modes of Eisenstein series
• Fourier expansions of Kac-Moody Eisenstein series and degenerate Whittaker vectors
• Global uniqueness of small representations
• A notion of rank for unitary representations of reductive groups based on Kirillov's orbit method
• Instanton corrections to the universal hypermultiplet and automorphic forms on \(\text{SU}(2,1)\)
• Modèles de Whittaker dégénéres pour des groupes p-adiques. (Degenerate Whittaker models of p-adic groups)
• Whittaker vectors and associated varieties
• The multiplicity one theorem for \(\mathrm{GL}_n\)
• Note on rational points in nilpotent orbits of semisimple groups
• Effects of D-instantons
• On the automorphic theta representation for simply laced groups
• Unity of superstring dualities.
• D-particle bound states and the D-instanton measure
• Exact \(\nabla^{4}\mathcal{R}^{4}\) couplings and helicity supertraces
• Fourier coefficients attached to small automorphic representations of \(\operatorname{SL}_n(\mathbb{A})\)
• Central extensions of reductive groups by \(K_2\).
• Picard-Lefschetz theory and characters of a semisimple Lie group
• D-particle bound states and generalized instantons
• Whittaker supports for representations of reductive groups
• Certain conjectures relating unipotent orbits to automorphic representations
• Towards a classification of global integral constructions and functorial liftings using the small representations method
• On a result of Moeglin and Waldspurger in residual characteristic 2
• On the modular structure of the genus-one type II superstring low energy expansion
• The automorphic NS5-brane
• Eisenstein Series and Automorphic Representations
• Eulerianity of Fourier coefficients of automorphic forms
• Generalized and degenerate Whittaker quotients and Fourier coefficients
• Generalized and degenerate Whittaker models
• Raising nilpotent orbits in wave-front sets

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