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A answer to your question is in Freundenthal Linear Lie groups, Academic press. Also in Lecture of Lie groups by Adams. Some of the books written by Helgason, have a complete answer too.
Sorry i confused you, i mean the book The Langlands classification and irreducible characters (D. Barbasch, J. Adams and D. Vogan), Birkhauser (1992), Boston-Basel-Berlin.