Publication details

Higher symmetries of symplectic Dirac operator

Authors

SOMBERG Petr ŠILHAN Josef

Year of publication 2020
Type Article in Periodical
Magazine / Source Geometriae Dedicata
MU Faculty or unit

Faculty of Science

Citation
Web https://doi.org/10.1007/s10711-020-00529-3
Doi http://dx.doi.org/10.1007/s10711-020-00529-3
Keywords Symplectic Dirac operator; Higher symmetry algebra; Projective differential geometry; Minimal nilpotent orbit; sl(3.R)
Description 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).
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