Geodesic
Standard Representations of Simple Lie Algebras
Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 344-361

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Let L be any simple finite-dimensional Lie algebra (defined over the field K of complex numbers). Cartan's theory of weights is used to define sets of (algebraic) representations of L that can be characterized in terms of left ideals of the universal enveloping algebra of L. These representations, called standard, generalize irreducible representations that possess a dominant weight. The newly obtained representations are all infinite-dimensional. Their study is initiated here by obtaining a partial solution to the problem of characterizing them by means of sequences of elements in K. 
Bouwer, I. Z. Standard Representations of Simple Lie Algebras. Canadian journal of mathematics, Tome 20 (1968) no. 1, pp. 344-361. doi: 10.4153/CJM-1968-031-5
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