We establish 2-jet determinacy for the symmetry algebra of the underlying structure of any (complex or real) parabolic geometry. At non-flat points, we prove that the symmetry algebra is in fact 1-jet determined. Moreover, we prove 1-jet determinacy at any point for a variety of non-flat parabolic geometries—in particular torsion-free, parabolic contact, and several other classes.
Mathematics Subject Classification
Primary 58D19 Secondary 57S25 58K70 22F30
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We thank J.M. Landsberg for discussions on minuscule varieties and sub-cominuscule representations. We are grateful to A. Isaev and I. Kossovskiy for information about the results on stability and linearization in CR-geometry. B.K. was supported by the University of Tromsø while visiting the Australian National University (where this work was initiated) and the University of Vienna. D.T. was supported by a Lise Meitner Fellowship (project M1884-N84) of the Austrian Science Fund (FWF).
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