Symplectic Killing spinors

Svatopluk Krýsl

Commentationes Mathematicae Universitatis Carolinae (2012)

  • Volume: 53, Issue: 1, page 19-35
  • ISSN: 0010-2628

Abstract

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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 ∇ . 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 may easily compute the symplectic Killing spinor fields for the standard symplectic vector spaces and the round sphere S 2 equipped with the volume form of the round metric.

How to cite

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Krýsl, Svatopluk. "Symplectic Killing spinors." Commentationes Mathematicae Universitatis Carolinae 53.1 (2012): 19-35. <http://eudml.org/doc/246174>.

@article{Krýsl2012,
abstract = {Let $(M,\omega )$ 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 may easily compute the symplectic Killing spinor fields for the standard symplectic vector spaces and the round sphere $S^2$ equipped with the volume form of the round metric.},
author = {Krýsl, Svatopluk},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Fedosov manifolds; symplectic spinors; symplectic Killing spinors; symplectic Dirac operators; Segal-Shale-Weil representation; Fedosov manifold; symplectic spinor; symplectic Killing spinor; symplectic Dirac operator; Segal-Shale-Weil representation},
language = {eng},
number = {1},
pages = {19-35},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Symplectic Killing spinors},
url = {http://eudml.org/doc/246174},
volume = {53},
year = {2012},
}

TY - JOUR
AU - Krýsl, Svatopluk
TI - Symplectic Killing spinors
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2012
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 53
IS - 1
SP - 19
EP - 35
AB - Let $(M,\omega )$ 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 may easily compute the symplectic Killing spinor fields for the standard symplectic vector spaces and the round sphere $S^2$ equipped with the volume form of the round metric.
LA - eng
KW - Fedosov manifolds; symplectic spinors; symplectic Killing spinors; symplectic Dirac operators; Segal-Shale-Weil representation; Fedosov manifold; symplectic spinor; symplectic Killing spinor; symplectic Dirac operator; Segal-Shale-Weil representation
UR - http://eudml.org/doc/246174
ER -

References

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  9. Krýsl S., Howe type duality for the metaplectic group acting on symplectic spinor valued forms, J. Lie Theory, to appear; electronically available at math.RT/0508.2904. 
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