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We give an account of the construction of exterior differential systems basedon the notion of tableaux over Lie algebras as developed in [Comm. Anal. Geom14 (2006), 475-496; math.DG/0412169]. The definition of a tableau over a Liealgebra is revisited and extended in the light of the formalism of the Spencercohomology; the question of involutiveness for the associated systems and theirprolongations is addressed; examples are discussed.

Differential systems associated with tableaux over Lie algebras