Higher symmetries of symplectic Dirac operator

Petr Somberg; Josef Šilhan

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arXiv · 1803.06970

Higher symmetries of symplectic Dirac operator

Petr Somberg·Josef Šilhan

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Abstract

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 $\mathfrak{sl}(3,{\mathbb{R}})$.

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Petr Somberg, Josef Šilhan. 2018-03-19. Higher symmetries of symplectic Dirac operator. https://arxiv.org/abs/1803.06970

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