  We prove a theorem relating the automorphism group of a Cartan geometry to
the group on which the geometry is modeled: a component of the adjoint
representation of the first embeds in the adjoint representation of the second.
Consequences of the theorem include general bounds on the rank and nilpotence
degree of an automorphism group; a result asserting local homogeneity and
completeness of parabolic geometries admitting a maximal-rank group of
automorphisms; and a local freeness theorem for actions additionally preserving
a continuous volume form.
