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Relation of the spectra of symplectic Rarita-Schwinger and Dirac operators on flat symplectic manifolds. (English) Zbl 1199.58011
Summary: Consider a flat symplectic manifold $$(M^{2l},\omega )$$, $$l\geq 2$$, 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 $$\lambda$$ 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.

##### MSC:
 58J05 Elliptic equations on manifolds, general theory 58J50 Spectral problems; spectral geometry; scattering theory on manifolds 35N10 Overdetermined systems of PDEs with variable coefficients 53D05 Symplectic manifolds (general theory)
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