Classification of extremally irreducible and normally irreducible representations of semisimple complex connected Lie groups

A new concept of “extremal irreducibility” for representations of Lie groups in separable locally convex spaces is introduced. All extremally irreducible representations of semisimple complex Lie groups are classified to within equivalence, i.e. to within topological isomorphism rearranging representation operators. Analogous results are obtained for other variants of axiomatics (normal irreducibility, Gel'fand irreducibility, complete irreducibility).