Jet-determination of symmetries of parabolic geometries

TL;DR

This paper proves that the symmetry algebra of parabolic geometries is determined by 2-jets in general and by 1-jets at non-flat points, with specific results for various classes of geometries.

Contribution

It establishes jet-determinacy results for the symmetry algebra of parabolic geometries, including 1-jet determination at non-flat points and for specific subclasses.

Findings

Symmetry algebra is 2-jet determined for all parabolic geometries.

At non-flat points, symmetry algebra is 1-jet determined.

1-jet determinacy holds at any point for certain classes like torsion-free and contact geometries.

Abstract

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.