A natural parameter of a curve in the symplectic space

R. Krasnodębski

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Consider a flat symplectic manifold $(M^{2 l}, ω)$ , $l \geq 2$ , 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 $- ı l λ$ is not a symplectic Killing number, then $\frac{l - 1}{l} λ$ is an eigenvalue of the symplectic Rarita-Schwinger operator.