Intertwining operators for iterated Dirac operators over Minkowski-type spaces
type: Item
instance of: scholarly article
title: Intertwining operators for iterated Dirac operators over Minkowski-type spaces
zbMATH Open document ID: 0791.15022
author: K. Appert
published in: Journal of Mathematical Analysis and Applications
publication date: 1993-09-05T00:00:00Z
review text: It is well known that the group of orientation preserving motions of a hyperbolic space can be described in terms of the corresponding Vahlen group. Generalizing this result the author shows how to describe the Möbius transformations of \(\mathbb{R}^{p,q}\) (with inner product \(\sum^ p_{j=1} x_ jy_ j-\sum^{p+q}_{j=p+1} x_ jy_ j)\) via a group \(V(p,q)\) of \((2 \times 2)\)-matrices whose entries belong to a Clifford algebra and satisfy suitable constraints. Vahlen groups over \(\mathbb{C}^ n\) are also discussed. In the final section the author investigates the equivariance properties of the Dirac operator over \(\mathbb{R}^{p,q}\) with respect to \(V(p,q)\) and a suitable conformal weight (automorphy factor). He also points out that some known results can now be extended to \(\mathbb{C}^ n\) and used to obtain an intertwining operator for the Plemelj formulae.
reviewed by: Jürgen Elstrodt
Mathematics Subject Classification ID: 15A66
Mathematics Subject Classification ID: 30G35
zbMATH DE Number: 399091
zbMATH Keywords: hyperbolic space
zbMATH Keywords: Vahlen group
zbMATH Keywords: Möbius transformations
zbMATH Keywords: Clifford algebra
zbMATH Keywords: Dirac operator
zbMATH Keywords: Plemelj formulae
MaRDI profile type: Publication
full work available at URL: jmaa.1993.1239
OpenAlex ID: W2065430972
DOI: 10.1006/JMAA.1993.1239
description: scientific article; zbMATH DE number 399091