Relation of the Spectra of Symplectic Rarita-schwinger and Dirac Operators on Flat Symplectic Manifolds

Consider a flat symplectic manifold (M, ω), l ≥ 2, admitting a metaplectic structure. We prove that the symplectic twistor operator maps the eigenvectors of the symplectic Dirac operator, that are not symplectic Killing spinors, to the eigenvectors of the symplectic Rarita-Schwinger operator. If λ is an eigenvalue of the symplectic Dirac operator such that −ılλ is not a symplectic Killing number, then l−1 l λ is an eigenvalue of the symplectic Rarita-Schwinger operator.