Fourier coefficients attached to small automorphic representations of \(\operatorname{SL}_n(\mathbb{A})\)

DOI10.1016/j.jnt.2018.03.022zbMath1443.11079arXiv1707.08937OpenAlexW2802676600MaRDI QIDQ1786688

Henrik P. A. Gustafsson, Baiying Liu, Axel Kleinschmidt, Daniel Persson, Olof Ahlén

Publication date: 24 September 2018

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1707.08937

zbMATH Keywords

Fourier expansionFourier coefficientssmall automorphic forms

Mathematics Subject Classification ID

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

Related Items (5)

Nilpotent orbits of orthogonal groups over \(p\)-adic fields, and the DeBacker parametrization ⋮ Whittaker supports for representations of reductive groups ⋮ Eulerianity of Fourier coefficients of automorphic forms ⋮ A reduction principle for Fourier coefficients of automorphic forms ⋮ Fourier coefficients of minimal and next-to-minimal automorphic representations of simply-laced groups

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• 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
• Eisenstein series for higher-rank groups and string theory amplitudes
• On nilpotent orbits of \(\mathrm{SL}_{n}\) and \(\mathrm{Sp}_{2n}\) over a local non-Archimedean field
• 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 \(\mathrm{GL}_n\)
• \(D\)-brane bound state redux
• On the automorphic theta representation for simply laced groups
• Witten index and threshold bound states of D-branes
• Unity of superstring dualities.
• Exact \(\nabla^{4}\mathcal{R}^{4}\) couplings and helicity supertraces
• Eisenstein series for infinite-dimensional U-duality groups
• D-particle bound states and generalized instantons
• Certain conjectures relating unipotent orbits to automorphic representations
• Protected couplings and BPS dyons in half-maximal supersymmetric string vacua
• On Certain L-Functions
• The minimal orbit in a simple Lie algebra and its associated maximal ideal
• On an explicit formula for class-$1$ “Whittaker functions” on $GL_n $ over $\beta $-adic fields
• Eisenstein Series and Automorphic Representations
• On Fourier Coefficients of Automorphic Forms of GL(n)
• Generalized and degenerate Whittaker models
• Raising nilpotent orbits in wave-front sets
• Lie groups beyond an introduction

This page was built for publication: Fourier coefficients attached to small automorphic representations of \(\operatorname{SL}_n(\mathbb{A})\)