Higher symmetries of symplectic Dirac operator

2018/03/19 by Somberg, Petr, Šilhan, Josef
#17B08 #35Q41 #53A20 #53D05 #58D19 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Representation Theory (math.RT) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1803.06970

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 \mathfraksl(3,ℝ).

Related

• Projective structure, \widetildeSL(3,\mathbb R) and the symplectic Dirac operator
• Clifford Homomorphisms and Higher Spin Dirac Operators
• Symplectic Dirac Operators on Hermitian Symmetric Spaces
• The higher spin Dirac operators
• Models for irreducible representations of the symplectic algebra using Dirac-type operators