symplectic spinors; Dirac operators; Mpc-structures; homogeneous spaces; lifting to Mpc
Résumé :
[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.
Disciplines :
Mathématiques
Auteur, co-auteur :
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
