Invariance of iterated global differential operator for slice monogenic functions

TL;DR

This paper investigates the symmetry properties and intertwining operators of the global slice Dirac operator and its variants, providing explicit forms and extending the operator to functions on the entire Euclidean space.

Contribution

It introduces the invariance group and explicit intertwining operators for the iterated global slice Dirac operator, and extends the operator to a broader class of functions.

Findings

Identified the symmetry group of the global slice Dirac operator.

Derived explicit forms of intertwining operators for the iterated operator.

Introduced a variant of the operator applicable to functions on all Euclidean space.

Abstract

In this article, we present the symmetry group of a global slice Dirac operator and its iterated ones. Further, the explicit forms of intertwining operators of the iterated global slice Dirac operator are given. At the end, we introduce a variant of the global slice Dirac operator, which allows functions considered to be defined on the whole Euclidean space. The invariance property and the intertwining operators of this variant of the global slice Dirac operator are also presented.