Tensor calculus in enveloping algebras

The technique of reduction of tensor products v ⊗ W of g-modules (g being a reductive complex Lie algebra), V being semi-simple finite-dimensional, by means of tensor calculus in the enveloping algebra U of g is exposed. It leads to considertations on Galois extensions of the center of U by the Weyl group of g. Its use in view of the study of the unitarizability of go-modules, go being a real form of g is indicated.