On Kazhdan's property (T) for Sp(k).
Bekka, M.B., Neuhauser, M. (2002)
Journal of Lie Theory
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Bekka, M.B., Neuhauser, M. (2002)
Journal of Lie Theory
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Svatopluk Krýsl (2007)
Archivum Mathematicum
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Consider a flat symplectic manifold , , 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 is an eigenvalue of the symplectic Dirac operator such that is not a symplectic Killing number, then is an eigenvalue of the symplectic Rarita-Schwinger operator.
Svatopluk Krýsl (2012)
Commentationes Mathematicae Universitatis Carolinae
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Let be a symplectic manifold admitting a metaplectic structure (a symplectic analogue of the Riemannian spin structure) and a torsion-free symplectic connection . Symplectic Killing spinor fields for this structure are sections of the symplectic spinor bundle satisfying a certain first order partial differential equation and they are the main object of this paper. We derive a necessary condition which has to be satisfied by a symplectic Killing spinor field. Using this condition one...
Marie Dostálová, Petr Somberg (2013)
Archivum Mathematicum
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We introduce the symplectic twistor operator in symplectic spin geometry of real dimension two, as a symplectic analogue of the Dolbeault operator in complex spin geometry of complex dimension 1. Based on the techniques of the metaplectic Howe duality and algebraic Weyl algebra, we compute the space of its solutions on .