On the Symplectic Structure of Coadjoint Orbits of (Solvable) Lie Groups and Applications. I.

Niels Vigand Pedersen

Displaying similar documents to “On the Symplectic Structure of Coadjoint Orbits of (Solvable) Lie Groups and Applications. I.”

The reduction of symplectic structure and Sternberg construction

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Symplectic strucutre on generalized orbits of solvable Lie groups.

L. Pukanszky (1984)

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Symplectic Killing spinors

Svatopluk Krýsl (2012)

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Let $(M, ω)$ be a symplectic manifold admitting a metaplectic structure (a symplectic analogue of the Riemannian spin structure) and a torsion-free symplectic connection $\nabla$ . 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...

Relation of the spectra of symplectic Rarita-Schwinger and Dirac operators on flat symplectic manifolds

Svatopluk Krýsl (2007)

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Consider a flat symplectic manifold $(M^{2 l}, ω)$ , $l \geq 2$ , 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 $λ$ is an eigenvalue of the symplectic Dirac operator such that $- ı l λ$ is not a symplectic Killing number, then $\frac{l - 1}{l} λ$ is an eigenvalue of the symplectic Rarita-Schwinger operator.