Geodesic
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

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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.
Classification : 35N10, 53D05, 58J05, 58J50, 58Jxx
Keywords: symplectic Dirac operator; symplectic Rarita-Schwinger operator; Kostant symplectic spinors 
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     author = {Kr\'ysl, Svatopluk},
     title = {Relation of the spectra of symplectic {Rarita-Schwinger} and {Dirac} operators on flat symplectic manifolds},
     journal = {Archivum mathematicum},
     pages = {467--484},
     publisher = {mathdoc},
     volume = {43},
     number = {5},
     year = {2007},
     mrnumber = {2381789},
     zbl = {1199.58011},
     language = {en},
     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/