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Mathematics > Differential Geometry

Title: 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 ${D}\kern-0.5em\raise0.22ex\hbox{/}_s$ 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 $\mathfrak{sl}(3,{\mathbb{R}})$.
Comments: Symplectic Dirac operator, Higher symmetry algebra, Projective differential geometry, Minimal nilpotent orbit, $\mathfrak{sl}(3,\mR)$
Subjects: Differential Geometry (math.DG); Mathematical Physics (math-ph); Functional Analysis (math.FA); Representation Theory (math.RT); Symplectic Geometry (math.SG)
MSC classes: 53D05, 35Q41, 58D19, 17B08, 53A20
Cite as: arXiv:1803.06970 [math.DG]
  (or arXiv:1803.06970v1 [math.DG] for this version)

Submission history

From: Petr Somberg [view email]
[v1] Mon, 19 Mar 2018 15:01:10 GMT (26kb)