  For various series of complex semi-simple Lie algebras $\fg (t)$ equipped
with irreducible representations $V(t)$, we decompose the tensor powers of
$V(t)$ into irreducible factors in a uniform manner, using a tool we call {\it
diagram induction}.
  In particular, we interpret the decompostion formulas of Deligne \cite{del}
and Vogel \cite{vog} for decomposing $\fg^{\ot k}$ respectively for the
exceptional series and $k\leq 4$ and all simple Lie algebras and $k\leq 3$, as
well as new formulas for the other rows of Freudenthal's magic chart.
  By working with Lie algebras augmented by the symmetry group of a marked
Dynkin diagram, we are able to extend the list \cite{brion} of modules for
which the algebra of invariant regular functions under a maximal nilpotent
subalgebra is a polynomial algebra. Diagram induction applied to the exterior
algebra furnishes new examples of distinct representations having the same
Casimir eigenvalue.
