On principal series Whittaker functions on \(\text{Sp}(2,\mathbb R)\)

DOI10.1016/j.jfa.2005.03.023zbMath1078.11031OpenAlexW2019492045MaRDI QIDQ2566235

Taku Ishii

Publication date: 22 September 2005

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2005.03.023

zbMATH Keywords

automorphic formsWhittaker functionprincipal series representation

Mathematics Subject Classification ID

Semisimple Lie groups and their representations (22E46) Siegel modular groups; Siegel and Hilbert-Siegel modular and automorphic forms (11F46) Confluent hypergeometric functions, Whittaker functions, ({}_1F_1) (33C15)

Related Items

Whittaker functions for generalized principal series representations of \(\mathrm{GSp}(2,\mathbb{R})\) ⋮ The \((\mathfrak g,K)\)-module structures of principal series of \(\text{SU}(2,2)\) ⋮ Whittaker functions for \(P_J\)-principal series representations of \(\text{Sp}(3,\mathbb R)\) ⋮ Principal series and generalized principal series Whittaker functions with peripheral \(K\)-types on the real symplectic group of rank 2 ⋮ A density theorem for Sp(4)$\operatorname{Sp}(4)$ ⋮ On Petersson norms of generic cusp forms and special values of adjoint L -functions for GSp4 ⋮ Spinor $L$-functions for generic cusp forms on $GSp(2)$ belonging to principal series representations ⋮ Calculus of principal series Whittaker functions on \(\mathrm{SL}(n, \mathbb R)\) ⋮ An explicit integral representation of Siegel-Whittaker functions on 𝑆𝑝(2,ℝ) for the large discrete series representations ⋮ Principal series Whittaker functions on \(Sp(2,\mathbb{C})\) ⋮ Secondary Whittaker functions for \(P_J\)-principal series representations of \(\text{Sp}(3,\mathbb R)\)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Whittaker functions on semisimple Lie groups
• 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
• Whittaker vectors and conical vectors
• The multiplicity one theorem for \(\mathrm{GL}_n\)
• Cubic metaplectic forms and theta functions
• Commutation relations of differential operators and Whittaker functions on \(\text{Sp}_ 2(\mathbb{R})\)
• Mellin transforms of GL ( n , [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /) whittaker functions]
• GL(4, ℝ)-Whittaker Functions and 4 F 3 (1) Hypergeometric Series
• Entireness of the Spinor L-functions for certain generic cusp forms on GSp(2)
• Fonctions de Whittaker associées aux groupes de Chevalley