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Connected Order 3 Standard Representations of Simple Lie Algebras

Published online by Cambridge University Press:  20 November 2018

F. W. Lemire
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The concept of standard representations of simple Lie algebras was introduced by I. Z. Bouwer [1], One of the difficulties was that of existence. The order zero standard representations are simply those having a dominant weight vector and these have been completely characterized, for example in [2].

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 3 , 01 September 1974 , pp. 381 - 383
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Bouwer, I. Z., Standard Representations of Simple Lie Algebras, Can. J. Math. 20 (1968), 344-361.Google Scholar
2. Harish-Chandna, , Some Applications of the Universal Enveloping Algebra of a Semi-Simple Lie Algebra, Trans. Amer. Math. Soc. 70 (1951), 28-96.Google Scholar
3. 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