| 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 ORBilu) | |
| 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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