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I am looking for a reference that describes how to decompose a tensor product of two finite dimensional simple modules for a reductive Lie algebra over $\mathbb{C}$.

In particular, I would like a reference that describes it along the same lines as the way it can be described for $gl_n(\mathbb{C})$ and $sl_n(\mathbb{C})$ (where it simply becomes a combinatorial question in that case involving the Littlewood-Richardson coefficients).

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up vote 2 down vote accepted

This has been fully discussed in

Decompose tensor product of type $G_2$ Lie algebras.

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