New formulas for Whittaker functions on \(\text{GL}(n,\mathbb R)\)
type: Item
instance of: scholarly article
title: New formulas for Whittaker functions on \(\text{GL}(n,\mathbb R)\)
zbMATH Open document ID: 1121.22003
author: Taku Ishii
author: Eric Stade
published in: Journal of Functional Analysis
publication date: 2007-05-10T00:00:00Z
review text: From the authors' abstract: We derive new recursive formulas for principal series Whittaker functions, of both fundamental and class one type, on \(\text{GL}(n,\mathbb R)\). These formulas relate such Whittaker functions to their counterparts on \(\text{GL}(n-1,\mathbb R)\), instead of on \(\text{GL}(n-2,\mathbb R)\) as has been the case in numerous earlier studies. In the particular case \(n=3\), and for certain special values of the eigenvalues, our formulas are seen to resemble classical summation formulas, due to Gegenbauer, for Bessel functions. To illuminate this resemblance we also derive, in this work, formulas for certain special values of \(\text{GL}(3,\mathbb R)\) fundamental Whittaker functions. These formulas may be understood as analogs of expressions derived by Bump and Friedberg for class one Whittaker functions on \(\text{GL}(3,\mathbb R)\).
reviewed by: Salah Mehdi
Mathematics Subject Classification ID: 22E45
Mathematics Subject Classification ID: 11F70
Mathematics Subject Classification ID: 43A80
Mathematics Subject Classification ID: 33C80
zbMATH DE Number: 5151620
zbMATH Keywords: linear group
zbMATH Keywords: Whittaker functions
MaRDI profile type: Publication
full work available at URL: j.jfa.2006.12.004
OpenAlex ID: W2012264678
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DOI: 10.1016/J.JFA.2006.12.004
description: scientific article; zbMATH DE number 5151620