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symplectic Dirac operator; symplectic Rarita-Schwinger operator; Kostant symplectic spinors
Consider a flat symplectic manifold $(M^{2l},\omega )$, $l\ge 2$, 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 $\lambda $ is an eigenvalue of the symplectic Dirac operator such that $-\imath l \lambda $ is not a symplectic Killing number, then $\frac{l-1}{l}\lambda $ is an eigenvalue of the symplectic Rarita-Schwinger operator.
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