Unramified Whittaker functions for \(GL(3,\mathbb{R})\)

DOI10.1007/BF02788764zbMath0839.22016OpenAlexW1979513726MaRDI QIDQ1899780

Yanyan Li

Publication date: 19 June 1996

Published in: Journal d'Analyse Mathématique (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02788764

zbMATH Keywords

integral representationeigenfunctionsdifferential operatorsWhittaker functionsdiagonal matricesunramified principal series representations

Mathematics Subject Classification ID

Connections of hypergeometric functions with groups and algebras, and related topics (33C80) Representations of Lie and linear algebraic groups over real fields: analytic methods (22E45)

Related Items (8)

Matrix Whittaker processes ⋮ Directed polymers and the quantum Toda lattice ⋮ Exponential functionals of Brownian motion and class-one Whittaker functions ⋮ Global decomposition of \(\operatorname{GL}(3)\) Kloosterman sums and the spectral large sieve ⋮ Evaluating Whittaker functions and Maass forms for 𝑆𝐿(3,ℤ) ⋮ Comparison of cusp forms on \(\text{GL}(3,{\mathbb Z})\) ⋮ On the nonexistence of automorphic eigenfunctions of exponential growth on \(\mathrm{SL}(3,\mathbb Z)\setminus \mathrm{SL}(3,\mathbb R)/\mathrm{SO}(3,\mathbb R)\) ⋮ The reciprocal of the beta function and \(GL(n,R)\) Whittaker functions

Cites Work

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• Automorphic forms on GL(3,\({\mathbb{R}})\)
• On explicit integral formulas for \(\text{GL}(n, \mathbb R)\)-Whittaker functions. With an appendix by Daniel Bump, Solomon Friedberg, and Jeffrey Hoffstein
• Poincaré series for GL(3,\({\mathbb{R}})\)-Whittaker functions
• On Mellin transforms of unramified Whittaker functions on GL(3,C)
• Theory of Eisenstein series for the group SL(3,R) and its application to a binary problem
• The multiplicity one theorem for \(\mathrm{GL}_n\)
• Fonctions de Whittaker associées aux groupes de Chevalley

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