  In the present paper we start the systematic explicit construction of
invariant differential operators by giving explicit description of one of the
main ingredients - the cuspidal parabolic subalgebras. We explicate also the
maximal parabolic subalgebras, since these are also important even when they
are not cuspidal. Our approach is easily generalised to the supersymmetric and
quantum group settings and is necessary for applications to string theory and
integrable models.
