On the determination of irreducible modules by restriction to a subalgebra

Lepowsky, J.; McCollum, G. W.

doi:10.1090/S0002-9947-1973-0323846-5

On the determination of irreducible modules by restriction to a subalgebra
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by J. Lepowsky and G. W. McCollum PDF

Trans. Amer. Math. Soc. 176 (1973), 45-57 Request permission

Abstract:

Let $\mathcal {B}$ be an algebra over a field, $\mathcal {A}$ a subalgebra of $\mathcal {B}$, and $\alpha$ an equivalence class of finite dimensional irreducible $\mathcal {A}$-modules. Under certain restrictions, bijections are established between the set of equivalence classes of irreducible $\mathcal {B}$-modules containing a nonzero $\alpha$-primary $\mathcal {A}$-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.

References

Éléments de mathématique

Groupes et algébres de Lie

Algébres de Lie

24

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