k-Dirac operator and parabolic geometries

TL;DR

This paper constructs invariant differential operators in parabolic geometries related to the k-Dirac operators, providing insights into their algebraic and geometric structures.

Contribution

It introduces a new class of invariant differential operators associated with parabolic geometries, extending the understanding of k-Dirac operators in Clifford analysis.

Findings

Constructed sequences of invariant differential operators.

Linked these operators to minimal resolutions of k-Dirac operators.

Enhanced the theoretical framework of parabolic geometries and Clifford analysis.

Abstract

The principal group of a Klein geometry has canonical left action on the homogeneous space of the geometry and this action induces action on the spaces of sections of vector bundles over the homogeneous space. This paper is about construction of differential operators invariant with respect to the induced action of the principal group of a particular type of parabolic geometry. These operators form sequences which are related to the minimal resolutions of the k-Dirac operators studied in Clifford analysis.