Symplectic spinor valued forms and invariant operators acting between them. (English) Zbl 1164.58320

Krýsl, Svatopluk

Arch. Math., Brno 42, No. 5, 279-290 (2006).

Summary: Exterior differential forms with values in the (Kostant’s) symplectic spinor bundle on a manifold with a given metaplectic structure are decomposed into invariant subspaces. Projections to these invariant subspaces of a covariant derivative associated to a torsion-free symplectic connection are described.

MSC:

58J60	Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.)
53C27	Spin and Spin\({}^c\) geometry
53D05	Symplectic manifolds (general theory)

Keywords:

symplectic geometry; symplectic spinors; metaplectic structure; higher symplectic spinor module; torsion-free connection