Intertwining operators for iterated Dirac operators over Minkowski-type spaces
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.
scientific article; zbMATH DE number 399091