Whittaker functions for the large discrete series representations of \(\mathrm{SU}(2,1)\) and related zeta integrals

DOI10.2977/prims/1195163592zbMath0867.11039OpenAlexW2064132246MaRDI QIDQ1918526

Takayuki Oda, Harutaka Koseki

Publication date: 21 August 1996

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2977/prims/1195163592

zbMATH Keywords

unitary groupMellin transformslocal zeta integralsarchimedean local \(L\)-factorHarish-Chandra parameterslarge discrete series representationspartial automorphic \(L\)-functionssmooth Whittaker functions

Mathematics Subject Classification ID

Analysis on real and complex Lie groups (22E30) Other groups and their modular and automorphic forms (several variables) (11F55) Representations of Lie and linear algebraic groups over real fields: analytic methods (22E45) Representation-theoretic methods; automorphic representations over local and global fields (11F70) Hecke-Petersson operators, differential operators (several variables) (11F60)

Related Items (5)

The Fourier expansion of modular forms on quaternionic exceptional groups ⋮ A comparison of automorphic \(L\)-functions in a theta series lifting for unitary groups ⋮ Modular forms on G 2 and their Standard L-Function ⋮ On epsilon factors attached to supercuspidal representations of unramified 𝑈(2,1) ⋮ The generalized Whittaker functions for \(SU\)(2,1) and the Fourier expansion of automorphic forms

Cites Work

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• 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
• Associated varieties and Gelfand-Kirillov dimensions for the discrete series of a semisimple Lie group
• An explicit integral representation of Whittaker functions on \(\text{Sp}(2;\mathbb{R})\) for the large discrete series representations
• Periods of Hilbert modular surfaces

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