Relation of the spectra of symplectic Rarita-Schwinger and Dirac operators on flat symplectic manifolds
Krýsl, Svatopluk
Archivum Mathematicum, Tome 043 (2007), p. 467-484 / Harvested from 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.

Publié le : 2007-01-01
Classification:  35N10,  53D05,  58J05,  58J50,  58Jxx 
@article{108085,
     author = {Svatopluk Kr\'ysl},
     title = {Relation of the spectra of symplectic Rarita-Schwinger and Dirac operators on flat symplectic manifolds},
     journal = {Archivum Mathematicum},
     volume = {043},
     year = {2007},
     pages = {467-484},
     zbl = {1199.58011},
     mrnumber = {2381789},
     language = {en},
     url = {http://dml.mathdoc.fr/item/108085}
}

Krýsl, Svatopluk. Relation of the spectra of symplectic Rarita-Schwinger and Dirac operators on flat symplectic manifolds. Archivum Mathematicum, Tome 043 (2007) pp. 467-484. http://gdmltest.u-ga.fr/item/108085/

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