RARITA-SCHWINGER OPERATOR AND HARMONIC POLYNOMIALS

YASUSHI HOMMA

Abstract : The Dirac operator is the first order differential operator acting on 1/2-spinor fields. It has many useful applications in geometry, global analysis, harmonic analysis, and physics. We can generalize the Dirac operator to the first order operators on other spinor fields with higher spin. For example, the operator on 3/2-spinor fields is called the Rarita-Schwinger operator, which is often used for the theory of realtivity. This RS operator has ellipticity and chirality. But its square is not Laplace type so that it is somewhat more difficult to get results for the RS operator than the Dirac operator.

In this talk, we give a result about polynomial solutions for the RS operator on ℝ^{n} from the viewpoint of representation theory.