Geodesic
H-Finite Irreducible Representations of Simple Lie Algebras
Canadian journal of mathematics, Tome 31 (1979) no. 5, pp. 1084-1106

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

Let L denote a simple Lie algebra over the complex number field C with H a fixed Cartan subalgebra and C(L) the centralizer of H in the universal enveloping algebra U of L. It is known [cf. 2, 5] that one can construct from each algebra homomorphism φ:C(L) → C a unique algebraically irreducible representation of L which admits a weight space decomposition relative to H in which the weight space corresponding to φ ↓ H ∈ H* is one-dimensional. Conversely, if (ρ, V) is an algebraically irreducible representation of L admitting a one-dimensional weight space Vλ for some λ ∈ H*, then there exists a unique algebra homomorphism φ:C(L) → C which extends λ such that (ρ, V) is equivalent to the representation constructed from φ. Any such representation will be said to be pointed. 
Lemire, F.; Pap, M. H-Finite Irreducible Representations of Simple Lie Algebras. Canadian journal of mathematics, Tome 31 (1979) no. 5, pp. 1084-1106. doi: 10.4153/CJM-1979-100-5
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