Geodesic
Beyond the Enveloping Algebra of sl 3
Canadian journal of mathematics, Tome 37 (1985) no. 4, pp. 710-729

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

The problem which motivated the writing of this paper is that of finding structure behind the decomposition of the sl 3 representation spaces V* ⊗ W = Hom(V, W) for finite dimensional irreducible sl 3-modules V and W. For sl 2 this extends the classical Clebsch-Gordon problem. The question has been considered for sl 3 in a computational way in [5]. In this paper we build a conceptual algebraic framework going beyond the enveloping algebra of sl 3.For each dominant integral weight α let V α be an irreducible representation of sl 3 of highest weight α. It is well known that, for weights α, μ, λ, the multiplicity of Vλ in Hom(Vα, Vα+μ ) is bounded by the multiplicity of μ in Vλ ,with equality for generic α. This suggests the possibility of a single construction of highest weight vectors of weight X in Hom(Vα, Vα+μ ) which is valid for all a. 
Flath, Daniel E.; Biedenharn, L. C. Beyond the Enveloping Algebra of sl 3. Canadian journal of mathematics, Tome 37 (1985) no. 4, pp. 710-729. doi: 10.4153/CJM-1985-038-9
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