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), 4557 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 HarishChandra and R. Godement in special cases. The general methods and results appear to be useful in the representation theory of semisimple Lie groups.References

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Additional Information
 © Copyright 1973 American Mathematical Society
 Journal: Trans. Amer. Math. Soc. 176 (1973), 4557
 MSC: Primary 17B10
 DOI: https://doi.org/10.1090/S00029947197303238465
 MathSciNet review: 0323846