Commutation relations of differential operators and Whittaker functions on \(\text{Sp}_ 2(\mathbb{R})\)
type: Item
instance of: scholarly article
title: Commutation relations of differential operators and Whittaker functions on \(\text{Sp}_ 2(\mathbb{R})\)
zbMATH Open document ID: 0868.11027
author: Shinji Niwa
published in: Proceedings of the Japan Academy. Series A
publication date: 1997-08-19T00:00:00Z
review text: The author considers the action of the dual pairs \(\text{Sp}_4 (\mathbb{R})\times (\text{SL}_2 (\mathbb{R})\times \text{SL}_2 (\mathbb{R}))\) and \(\text{Sp}_4 (\mathbb{R})\times \text{SL}_4(\mathbb{R})\) on the Weil representation; note that \(\text{SL}_2(\mathbb{R})\times \text{SL}_2 (\mathbb{R})\) is isogenous to \(\text{SO}(2,2)\) and \(\text{SL}_4 (\mathbb{R})\) is isogenous to \(\text{SO}(3,3)\). With the help of computer algebra the author calculates the actions of the corresponding universal enveloping algebras on the Weil representation. Using the global Weil representation he deduces a (known) formula for Whittaker functions on \(\text{Sp}_4 (\mathbb{R})\). Finally he determines the Mellin transform of this function.
Mathematics Subject Classification ID: 11F70
Mathematics Subject Classification ID: 22E55
zbMATH DE Number: 897686
zbMATH Keywords: commutation relations of differential operators
zbMATH Keywords: Weil representation
zbMATH Keywords: formula for Whittaker functions
zbMATH Keywords: Mellin transform
reviewed by: Samuel James Patterson
MaRDI profile type: Publication
full work available at URL: pjaa.71.189
OpenAlex ID: W2031463242
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DOI: 10.3792/PJAA.71.189
description: scientific article; zbMATH DE number 897686