Principal series Whittaker functions on \(\operatorname {Sp}(2;\mathbb{R})\). II
type: Item
instance of: scholarly article
title: Principal series Whittaker functions on \(\operatorname {Sp}(2;\mathbb{R})\). II
zbMATH Open document ID: 1003.11020
author: Takuya Miyazaki
author: Takayuki Oda
published in: Tôhoku Mathematical Journal. Second Series
publication date: 2003-01-20T00:00:00Z
review text: The authors obtain explicit formulae for the radial part of the Whittaker functions on \(G= \text{Sp} (2,\mathbb{R})\) belonging to principal series representations induced from the maximal parabolic of \(G\) associated to the long simple root. The characterization of the radial part of these functions follows from a detailed study of the action of Schmid's differential operators on spaces of Whittaker functions of a given \(K\)-type. The authors have previous results of this nature for Whittaker functions attached to various admissible representations of the real symplectic group of rank 2 [see Automorphic forms and related topics, Seoul 1993, 59-92 (1994; Zbl 0958.11037)].
Mathematics Subject Classification ID: 11F70
Mathematics Subject Classification ID: 22E45
zbMATH DE Number: 1230535
zbMATH Keywords: explicit formulae
zbMATH Keywords: radial part
zbMATH Keywords: Whittaker functions
zbMATH Keywords: principal series representations
reviewed by: L. Barchini
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178224977
OpenAlex ID: W2009479139
cites work: Q3741813
cites work: On Whittaker vectors and representation theory
cites work: Principal series Whittaker functions on \(\text{Sp}(2;{\mathbb{R}})\). Explicit formulae of differential equations
cites work: An explicit integral representation of Whittaker functions on \(\text{Sp}(2;\mathbb{R})\) for the large discrete series representations
cites work: Q5642743
cites work: Representations of real reductive Lie groups
cites work: Q3346501
cites work: Whittaker functions of generalized principal series on \(\mathrm{SU}(2,2)\)
DOI: 10.2748/TMJ/1178224977
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description: scientific article; zbMATH DE number 1230535