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

中文翻译：

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辛狄拉克算子的高对称性

我们构造了作用于辛旋量的辛狄拉克算子的实维 2 高对称代数的射影微分几何。高对称微分算子对应于一类任意高阶的射影不变超定算子作用于对称张量的解空间。高对称代数结构对应于一个完全素数的原始理想，它的相关变体是 $${\mathfrak {sl}}(3,{\mathbb {R}})$$ sl ( 3 , R ) 的最小幂零轨道.