Geodesic
Calculating Cartan spaces for affine homogeneous spaces
Sbornik. Mathematics, Tome 198 (2007) no. 10, pp. 1407-1431 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $G$ be a connected reductive algebraic group and $H$ a reductive subgroup of it. Fix a Borel subgroup $B$ of $G$ and a maximal torus $T\subset B$. The Cartan subspace $\mathfrak a_{G,G/H}$ is by definition a subspace of $\mathfrak t^*$ (where $\mathfrak t$ is the Lie algebra of the group $T$) spanned by the weights of all the $B$-semi-invariant rational functions on $G/H$. The spaces $\mathfrak a_{G,G/H}$ are calculated in this paper. Bibliography: 16 titles. 
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I. V. Losev. Calculating Cartan spaces for affine homogeneous spaces. Sbornik. Mathematics, Tome 198 (2007) no. 10, pp. 1407-1431. http://geodesic.mathdoc.fr/item/SM_2007_198_10_a1/

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