  We construct in projective differential geometry of the real dimension $2$
higher symmetry algebra of the symplectic Dirac operator
${D}\kern-0.5em\raise0.22ex\hbox{/}_s$ 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 $\mathfrak{sl}(3,{\mathbb{R}})$.
