Article (Scientific journals)
On Mpc-structures and symplectic Dirac operators
Cahen, Michel; Gutt, Simone; LA FUENTE-GRAVY, Laurent et al.
2014In Journal of Geometry and Physics, 86, p. 434-466
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Keywords :
symplectic spinors; Dirac operators; Mpc-structures; homogeneous spaces; lifting to Mpc
Abstract :
[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 :
Mathematics
Author, co-author :
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
External co-authors :
yes
Language :
English
Title :
On Mpc-structures and symplectic Dirac operators
Publication date :
2014
Journal title :
Journal of Geometry and Physics
ISSN :
0393-0440
Publisher :
Elsevier, Amsterdam, Netherlands
Volume :
86
Pages :
434-466
Peer reviewed :
Peer Reviewed verified by ORBi
Available on ORBilu :
since 16 November 2018

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