On the determination of irreducible modules by restriction to a subalgebra

Let B be an algebra over a field, Ã a subalgebra of $, and CL an equivalence class of finite dimensional irreducible Ã-modules. Under certain restrictions, bisections are established between the set of equivalence classes of irreducible a-modules containing a nonzero a-primary B-submodule, and the sets of equivalence classes of all irreducible modules of certain canonically constructed algebras. Related results had been obtained by Harish-Chandra and R. Godement in special cases. The general methods and results appear to be useful in the representation theory of semisimple Lie groups. enveloping algebra, Po in care-Birkhoff-Witt theorem, simple ring, full matrix algebra.