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An Irreducible Representation of sl(2)

Published online by Cambridge University Press:  20 November 2018

F.W. Lemire
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In a recent paper [1] MM. Arnal and Pinczon have classified all complex irreducible representations (ρ, V) of sl(2) having the property (P) that there exists a non-zero element x∈sl(2) such that ρ(x) admits an eigenvalue. It is the purpose of this note to demonstrate, by example, that there exist irreducible representations of sl(2) which do not have property (P). As usual, we consider sl(2) embedded in its universal enveloping algebra U and identify the representations of sl(2) and U.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 1 , 01 March 1974 , pp. 63 - 65
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Arnal, D. and Pinczon, G., “Sur certaines representations de l'algébre de Lie sl(2)”, C.R. Acad. Sc. Paris, t. 272 (1971). pp. 1369–72.Google Scholar
2. Jacobson, N., “Lie Algebras”, Interscience Publishers, 1962.Google Scholar