Symplectic spinor valued forms and invariant operators acting between them

TL;DR

This paper studies the decomposition of symplectic spinor-valued forms on manifolds with metaplectic structures and describes invariant projections of covariant derivatives acting on them.

Contribution

It introduces a decomposition of symplectic spinor-valued forms into invariant subspaces and characterizes the projections of covariant derivatives onto these subspaces.

Findings

Decomposition of forms into invariant subspaces.

Explicit description of projections of covariant derivatives.

Framework for analyzing invariant operators on symplectic spinor bundles.

Abstract

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.