Classification of Irreducible Unitary Representations of Compact Simple Lie Groups. I

An irreducible unitary representation of any group belongs to one of the three Wigner classes, potentially real, pseudo-real, or complex. The irreducible unitary representations of all the compact simple Lie groups except those of the type E are hereby classified. The similar classification for the simple groups E6, E7, and E8 is completed in the next paper.