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 mailto [Université Libre de Bruxelles - ULB > Mathematics]
Gutt, Simone mailto [Université Libre de Bruxelles - ULB > Mathematics]
La Fuente-Gravy, Laurent mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Rawnsley, John mailto [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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