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Existence of Weight Space Decompositions for Irreducible Representations of Simple Lie Algebras

Published online by Cambridge University Press:  20 November 2018

F. W. Lemire
F. W. Lemire*
Affiliation:
University of Windsor, Windsor, Ontario
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Let L denote a finite-dimensional simple Lie algebra over an algebraically closed field K of characteristic zero. It is well known that every finite-dimension 1, irreducible representation of L admits a weight space decomposition; moreover every irreducible representation of L having at least one weight space admits a weight space decomposition.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 14 , Issue 1 , January 1971 , pp. 113 - 115
Copyright
Copyright © Canadian Mathematical Society 1971

References

1. Bourbaki, N., Groupes et algèbres de Lie, Hermann, Paris, 1960.Google Scholar
2. Bouwer, I. Z., Standard representations of simple Lie algebras, Canad. J. Math. 20 (1968), 344-361.Google Scholar
3. Harish-Chandra, , On some applications of the universal enveloping algebra of a semisimple Lie algebra, Trans. Amer. Math. Soc. 70 (1951), 28-96.Google Scholar
4. Lemire, F. W., Irreducible representations of a simple Lie algebra admitting a one-dimensional weight space, Proc. Amer. Math. Soc. 19 (1968), 1161-1164.Google Scholar
5. Lemire, F. W., Weight spaces and irreducible representations of simple Lie algebras, Proc. Amer. Math. Soc. 22 (1969), 192-197.Google Scholar
6.Sophus Lie Séminaire, Théorie des algèbres de Lie, Topologie des groupes de Lie, Paris, 1955.Google Scholar