Let $\mathfrak g$ be a real simple noncompact Lie algebra. Are there any correspondence between irreducible real representations of $\mathfrak g$ and the highest weight correspond to some positive system of restricted roots.
There is a complete classification of the complex representation $\mathfrak g \otimes \mathbb C$. There is a classification of real irreducible representations using the irreducible representations of $\mathfrak g\otimes \mathbb C$ in "Onishchik, Lectures on real semi simple lie algebras and their representations". But in a paper I read, it is claimed that the real representations can also be classified using highest weight like complex one. But I can not find a reference for that.