Reference : On Mpc-structures and symplectic Dirac operators |

Scientific journals : Article | |||

Physical, chemical, mathematical & earth Sciences : Mathematics | |||

http://hdl.handle.net/10993/37312 | |||

On Mpc-structures and symplectic Dirac operators | |

English | |

Cahen, Michel [Université Libre de Bruxelles - ULB > Mathematics] | |

Gutt, Simone [Université Libre de Bruxelles - ULB > Mathematics] | |

La Fuente-Gravy, Laurent [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >] | |

Rawnsley, John [University of Warwick > Mathematics Institute] | |

2014 | |

Journal of Geometry and Physics | |

Elsevier | |

86 | |

434-466 | |

Yes (verified by ORBi^{lu}) | |

International | |

0393-0440 | |

Amsterdam | |

Netherlands | |

[en] symplectic spinors ; Dirac operators ; Mpc-structures ; homogeneous spaces ; lifting to Mpc | |

[en] We prove that the kernels of the restrictions of the symplectic Dirac operator and one
of the two symplectic Dirac–Dolbeault operators on natural sub-bundles of polynomial valued spinor fields are finite dimensional on a compact symplectic manifold. We compute these kernels explicitly for complex projective spaces and show that the remaining Dirac–Dolbeault operator has infinite dimensional kernels on these finite rank sub-bundles. We construct injections of subgroups of the symplectic group (the pseudo-unitary group and the stabiliser of a Lagrangian subspace) in the Mpc group and classify G-invariant Mpc-structures on symplectic manifolds with a G-action. We prove a variant of Parthasarathy’s formula for the commutator of two symplectic Dirac-type operators on general symmetric symplectic spaces. | |

http://hdl.handle.net/10993/37312 | |

10.1016/j.geomphys.2014.09.006 |

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