Some Rarita-Schwinger Type Operators

TL;DR

This paper generalizes Rarita-Schwinger operators, constructs their fundamental solutions, explores their integral formulas, and demonstrates conformal invariance and intertwining operators under conformal group actions.

Contribution

It introduces a broad class of Rarita-Schwinger type operators, providing fundamental solutions and analyzing their conformal invariance and related intertwining operators.

Findings

Constructed fundamental solutions for generalized Rarita-Schwinger operators

Established conformal invariance of projection operators and equations

Derived intertwining operators under conformal group actions

Abstract

In this paper we study a generalization of the classical Rarita-Schwinger type operators and construct their fundamental solutions. We give some basic integral formulas related to these operators. We also establish that the projection operators appearing in the Rarita-Schwinger operators and the Rarita-Schwinger equations are conformally invariant. We further obtain the intertwining operators for other operators related to the Rarita-Schwinger operators under actions of the conformal group.