The kernel of the Rarita-Schwinger operator on Riemannian spin manifolds

Uwe Semmelmann (Stuttgart)

Abstract: The Rarita-Schwinger operator is a twisted Dirac operator. 
It has several interesting applications in physics and differential 
geometry. In my talk I will introduce this operator, give some of 
its properties and then concentrate on its kernel. In contrast to 
the classical Dirac operator the Rarita-Schwinger operator can have 
a non-trivial kernel on compact manifolds with positive scalar curvature. 
I will discuss several examples and in particular explain how one can 
identify the kernel of the Rarita-Schwinger operator with subspaces 
of harmonic forms on manifolds with special holonomy. 

My talk is based on a joint work with Yasushi Homma (Waseda University, Tokyo).