On the determination of irreducible modules by restriction to a subalgebra

J. Lepowsky, G. W. McCollum

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32 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)45-57
Number of pages13
JournalTransactions of the American Mathematical Society
Volume176
DOIs
StatePublished - Feb 1973
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Mathematics
  • Applied Mathematics

Keywords

  • Absolutely irreducible module
  • Extension of submodules
  • Finitely semisimple module
  • Irreducible module
  • Irreducible representation
  • Lie algebra
  • Primary submodule
  • Universal

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