  We give an account of the construction of exterior differential systems based
on the notion of tableaux over Lie algebras as developed in [Comm. Anal. Geom
14 (2006), 475-496; math.DG/0412169]. The definition of a tableau over a Lie
algebra is revisited and extended in the light of the formalism of the Spencer
cohomology; the question of involutiveness for the associated systems and their
prolongations is addressed; examples are discussed.
