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.
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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