Geodesic
Smooth vectors forhighest weight representations
Glasgow mathematical journal, Tome 42 (2000) no. 3, pp. 469-477

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

Let(π_{λ}, H_{λ}) be a unitary highest weight representation ofthe connected Lie group G and g its Lie algebra. Theng contains an invariant closed convex cone W_{\rm{max}}such that, for each X∈W_{\rm{max}}^0, the selfadjoint operatori·dπ_{λ}(X) is bounded from above. We show that for each suchX, the space H_{λ}^{∞} of smooth vectors forthe action of G on H_{λ} coincides with the setD^{∞}(dπ_{λ}(X)) of smooth vectors for the generally unboundedoperator dπ_{λ}(X). 
Neeb, Karl-Hermann. Smooth vectors forhighest weight representations. Glasgow mathematical journal, Tome 42 (2000) no. 3, pp. 469-477. doi: 10.1017/S0017089500030135
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