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A New Family of Irreducible Representations of An

Published online by Cambridge University Press:  20 November 2018

F. W. Lemire
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For a simple Lie algebra L over the complex numbers ℂ all irreducible representations admitting a highest weight have been constructed and characterized for example in [3, 6]. In [1] Bouwer considered the family of all irreducible representations of L admitting at least one one-dimensional weight space (this includes, of course, all those having a highest weight space) and showed, by construction, that this is a strictly larger class of representations.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 18 , Issue 4 , October 1975 , pp. 543 - 546
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Bouwer, I. Z., Standard Representations of Simple Lie Algebras, Canad. J. Math. 70 (1968) 344–361.Google Scholar
2. Freudenthal, H., de Vries, H., Linear Lie Groups, London-New York: Academic Press 1969.Google Scholar
3. Harish-Chandra, , Some applications of the universal enveloping algebra of a semi-simple Lie algebra, Trans. Amer. Math. Soc. 70 (1951), 28–99.Google Scholar
4. Lemire, F. W., Weight Spaces and Irreducible Representations of Simple Lie Algebras, Proc. Amer. Math. Soc. 22 (1969), 192–197.Google Scholar
5. Lemire, F. W., One-dimensional Representations of the Cycle Subalgebra of a Semi-simple Lie Algebra, Canad. Math. Bull. 13 (1970), 463–467.Google Scholar
6. Lie, Séminaire Sophus, Théorie des algébres de Lie Topologie des groupes Lie, Paris: Ecole Norm. Sup. 1954–55.Google Scholar