What is a good reference to learn about real representations of Lie groups ? I've parsed through the very enlightening book of Fulton and Harris, but it is extremely (if not exclusively) exampleoriented, and I need the more general statements. More precisely, I'm looking for statements about the dimension of real irreducible representations of real Lie groups.
MR2041548 Onishchik, Arkady L. Lectures on real semisimple Lie algebras and their representations. ESI Lectures in Mathematics and Physics. European Mathematical Society (EMS), Zürich, 2004. x+86 pp. 


$\mathbb{R}$
may not mean irreducible over$\mathbb{C}$
. There are lots of textbooks, but what works best depends on what you know. – Jim Humphreys May 17 '13 at 21:21