Higher symmetries of symplectic Dirac operator
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|Symplectic Dirac operator; Higher symmetry algebra; Projective differential geometry; Minimal nilpotent orbit; sl(3.R)
|We construct in projective differential geometry of the real dimension 2 higher symmetry algebra of the symplectic Dirac operator D-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 sl(3,R).