Higher symmetries of symplectic Dirac operator

Abstract

We construct in projective differential geometry of the real dimension 2 higher symmetry algebra of the symplectic Dirac operator acting on symplectic spinors. The higher symmetry differential operators correspond to the solution space of a class of projectively invariant overdetermined operators of arbitrarily high order acting on symmetric tensors.

The higher symmetry algebra structure corresponds to a completely prime primitive ideal having as its associated variety the minimal nilpotent orbit of sl(3,R).

Keywords

• Symplectic Dirac operator
• Higher symmetry algebra
• Projective differential geometry
• Minimal nilpotent orbit