The rarita—schwinger operator and spherical monogenic forms

Abstract

There is a certain family of conformally invariant first order elliptic systems which include the Dirac operator as its first member, and the Rarita-Schwinger operator, as the second simplest operator in the row. Its basic properties on general spin manifolds are described there. The aim of the paper is to do first step towards a function theory for Rarita-Schwinger equation. The main result contained in the paper is a complete classification of polynomial solutions of Rarita-Schwinger equation on R n . Relations with Clifford analysis and representation theory are discussed.