The generalized Whittaker functions for several admissible representations of \(Sp(2,\mathbb{R})\)

DOI10.3792/PJAA.73.130zbMath0905.11025OpenAlexW2019726849MaRDI QIDQ1387936

Takuya Miyazaki

Publication date: 18 January 1999

Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3792/pjaa.73.130

zbMATH Keywords

Mellin transformshift operatorgeneralized Whittaker functionspin \(L\)-functionadmissible representations of the rank two symplectic group

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) Representations of Lie and linear algebraic groups over global fields and adèle rings (22E55)

Cites Work

• Finite multiplicity theorems for induced representations of semisimple Lie groups. I
• Finite multiplicity theorems for induced representations of semisimple Lie groups. II: Applications to generalized Gelfand-Graev representations
• A proof of Blattner's conjecture
• An explicit integral representation of Whittaker functions on \(\text{Sp}(2;\mathbb{R})\) for the large discrete series representations
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