I encountered a statement in a book:
Another important property of the tensor product of representations of simple Lie Algebras is that the tensor product of two irreducible representations $R$ and $R'$ contains the singlet, i.e. the trivial one-dimensional representation, at most once as a submodule.
Subsequently, it says
it does contain the singlet precisely in the case when $R'$ is the representation $R^+(g):=-(R(g))^t$ conjugate to $R$.
How to understand and prove these statements?