Structure of the tensor product semigroup

We study structure of the semigroup Tens(G) consisting of triples of dominant weights (\lambda,\mu,\nu) of a complex reductive Lie group G such that the triple tensor product of the corresponding irreducible representations of G has a nonzero G-invariant vector. We prove two general structural results for Tens(G) and give an explicit computation of Tens(G) for G=Sp(4,C) and G=G_2.