Geodesic
Picard groups of homogeneous spaces of linear algebraic groups and one-dimensional homogeneous vector bundles
Izvestiya. Mathematics , Tome 8 (1974) no. 2, pp. 301-327.

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We construct models of finite-dimensional linear and projective irreducible representations of a connected semisimple group $G$ in linear systems on the variety $G$. We establish an algebro-geometric criterion for the linearizability of an irreducible projective representation of $G$. We explain the algebro-geometric meaning of the numerical characteristic of an arbitrary rational character of a maximal torus of $G$. Using these results we compute the Picard group of an arbitrary homogeneous space of any connected linear algebraic group $H$, prove the homogeneity of an arbitrary one-dimensional algebraic vector bundle over such a space relative to some covering group of $H$, and compute the Chern class of such a bundle. 
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V. L. Popov. Picard groups of homogeneous spaces of linear algebraic groups and one-dimensional homogeneous vector bundles. Izvestiya. Mathematics , Tome 8 (1974) no. 2, pp. 301-327. http://geodesic.mathdoc.fr/item/IM2_1974_8_2_a3/

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