Lie algebras of difference-differential operators and Appell functions \(F_ 1\)
type: Item
instance of: scholarly article
title: Lie algebras of difference-differential operators and Appell functions \(F_ 1\)
zbMATH Open document ID: 0674.33010
DOI: 10.1016/0022-247X(89)90305-3
author: H. L. Manocha
published in: Journal of Mathematical Analysis and Applications
publication date: 1989-01-01T00:00:00Z
review text: This work makes use of the key observation that the Appell function \(F_ 1\) has the property of being the Mellin transform of the confluent hypergeometric function \({}_ 1F_ 1\) and that the functions \({}_ 1F_ 1\) act as basis vectors in certain models of irreducible representations of sl(2,\({\mathbb{C}})\) and G(0,1) (oscillator algebra). This result in new models of irreducible representations of these algebras in terms of difference-differential operators with the functions \(F_ 1\) playing the role of basis vectors. These models are exponentiated to the corresponding Lie groups SL(2,\({\mathbb{C}})\) and G(0,1). Using Weisners method new identities are obtained.
Mathematics Subject Classification ID: 33C80
Mathematics Subject Classification ID: 33C05
zbMATH DE Number: 4103466
zbMATH Keywords: Appell function
zbMATH Keywords: Mellin transform
zbMATH Keywords: difference-differential operators
MaRDI profile type: Publication
cites work: The Lie Theory of Two-Variable Hypergeometric Functions
cites work: Harmonic Analysis and Expansion Formulas for Two-Variable Hypergeometric Functions
cites work: Lie theory and special functions
cites work: Lie Theory and the Appell Functions $F_1 $
cites work: Q3319049
cites work: Group-theoretic origin of certain generating functions
full work available at URL: 0022-247x(89)90305-3
OpenAlex ID: W2076052674
description: scientific article; zbMATH DE number 4103466