An explicit integral representation of Whittaker functions on \(\text{Sp}(2;\mathbb{R})\) for the large discrete series representations

DOI10.2748/tmj/1178225761zbMath0812.11033OpenAlexW1733933781MaRDI QIDQ1335559

Takayuki Oda

Publication date: 16 October 1994

Published in: Tôhoku Mathematical Journal. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2748/tmj/1178225761

zbMATH Keywords

Whittaker functionsdiscrete series representations\(\text{Sp} (2,\mathbb{R})\) (of rank 2)

Mathematics Subject Classification ID

Representations of Lie and linear algebraic groups over real fields: analytic methods (22E45) Representation-theoretic methods; automorphic representations over local and global fields (11F70)

Related Items (14)

Whittaker functions for generalized principal series representations of \(\mathrm{GSp}(2,\mathbb{R})\) ⋮ Whittaker functions for \(P_J\)-principal series representations of \(\text{Sp}(3,\mathbb R)\) ⋮ Commutation relations of differential operators and Whittaker functions on \(\text{Sp}_ 2(\mathbb{R})\) ⋮ Whittaker functions for the large discrete series representations of \(\mathrm{SU}(2,1)\) and related zeta integrals ⋮ Differential equations for principal series Whittaker functions on \(SU(2,2)\) ⋮ The generalized Whittaker functions for several admissible representations of \(Sp(2,\mathbb{R})\) ⋮ Principal series and generalized principal series Whittaker functions with peripheral \(K\)-types on the real symplectic group of rank 2 ⋮ On Petersson norms of generic cusp forms and special values of adjoint L -functions for GSp4 ⋮ An explicit integral representation of Siegel-Whittaker functions on 𝑆𝑝(2,ℝ) for the large discrete series representations ⋮ SUR LES PAQUETS D’ARTHUR DE CONTENANT DES MODULES UNITAIRES DE PLUS HAUT POIDS, SCALAIRES ⋮ MATRIX COEFFICIENTS OF REPRESENTATIONS OF SU(2,2): THE CASE OF P_J-PRINCIPAL SERIES ⋮ Principal series Whittaker functions on \(Sp(2,\mathbb{C})\) ⋮ Principal series Whittaker functions on \(\operatorname {Sp}(2;\mathbb{R})\). II ⋮ Unnamed Item

Cites Work

• Embeddings of discrete series into induced representations of semisimple Lie groups. II: Generalized Whittaker models for \(SU(2,2)\)
• The multiplicity one theorem for \(\mathrm{GL}_n\)
• A proof of Blattner's conjecture
• Gelfand-Kirillov dimension for Harish-Chandra modules
• On Whittaker vectors and representation theory
• Automorphic forms on GL (2)
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