par Cahen, Michel 
;Gutt, Simone ;La Fuente Gravy, Laurent ;Rawnsley, John
Référence Journal of geometry and physics
Publication A Paraître, 2014
;Gutt, Simone ;La Fuente Gravy, Laurent ;Rawnsley, JohnRéférence Journal of geometry and physics
Publication A Paraître, 2014
Article révisé par les pairs
| Résumé : | 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. |
