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Relation of the spectra of symplectic Rarita-Schwinger and Dirac operators on flat symplectic manifolds
Archivum mathematicum, Tome 43 (2007) no. 5, pp. 467-484 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 35N10, 53D05, 58J05, 58J50, 58Jxx
Keywords: symplectic Dirac operator; symplectic Rarita-Schwinger operator; Kostant symplectic spinors 
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     title = {Relation of the spectra of symplectic {Rarita-Schwinger} and {Dirac} operators on flat symplectic manifolds},
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     url = {http://geodesic.mathdoc.fr/item/ARM_2007_43_5_a10/}
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Krýsl, Svatopluk. Relation of the spectra of symplectic Rarita-Schwinger and Dirac operators on flat symplectic manifolds. Archivum mathematicum, Tome 43 (2007) no. 5, pp. 467-484. http://geodesic.mathdoc.fr/item/ARM_2007_43_5_a10/

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