  This paper establishes three relations between the Toda field theory
associated to a simple Lie algebra and the integral curves of the standard
differential system on the corresponding complete flag variety. The motivation
comes from the viewpoint on the Toda field theories as Darboux integrable
differential systems as developed in \cite{AFV}. First, we establish an
isomorphism concerning regular functions on the jet space and on the unipotent
subgroup in the setting of a simple Lie group. Using this result, we then show
that in the sense of differential systems, after restricting one independent
variable to a constant the Toda field theory becomes the system for integral
curves of the standard differential system on a complete flag variety. Finally,
we establish that, in terms of differential invariants, the Toda field theory
is the quotient of the product of two such systems by a natural group action.
