On one hand, in reading Georgi's book in group theory, I comprehend the invariant tensor as a special "tensor", which is unchanged under the action of any generators. On the other hand, CG decomposition is to decompose the product of two irreps into different irreps. Now it is claimed that invariant tensors are Clebsch-Gordan coupling constants for the product of two irreps. Why? Thank you very much for your answer!