For compact Lie groups one considers a maximal torus to define the weight space decomposition of a representation. For a complex semisimple Lie algebra one considers a Cartan subalgebra. How does one define weights for a general semisimple Lie group?
According to wikipedia the irreducible representations of semisimple Lie groups are parametrized by highest weights. Can anyone confirm that this is indeed true and shed any light on this theory?