Cyclic modules for a complex semisimple Lie group

We consider cyclic modules generated by elementary representations of a complex semisimple Lie group. The main result is a theorem on cyclicity (Theorem 3 of § 4), according to which the elementary representations are generated by cyclic vectors of a special type with respect to a maximal compact subgroup. We give a classification of completely irreducible representations in terms of the characteristic (highest and lowest) weights.