Geodesic
A New Family of Irreducible Representations of An
Canadian mathematical bulletin, Tome 18 (1975) no. 4, pp. 543-546

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
A New Family of Irreducible Representations of An. Canadian mathematical bulletin, Tome 18 (1975) no. 4, pp. 543-546. doi: 10.4153/CMB-1975-098-4
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[1] 1. Bouwer, I. Z., Standard Representations of Simple Lie Algebras, Canad. J. Math. 70 (1968) 344–361. Google Scholar

[2] 2. Freudenthal, H., de Vries, H., Linear Lie Groups, London-New York: Academic Press 1969. Google Scholar

[3] 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] 4. Lemire, F. W., Weight Spaces and Irreducible Representations of Simple Lie Algebras, Proc. Amer. Math. Soc. 22 (1969), 192–197. Google Scholar

[5] 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] 6. Lie, Séminaire Sophus, Théorie des algébres de Lie Topologie des groupes Lie, Paris: Ecole Norm. Sup. 1954–55. Google Scholar

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