Computation of the Cartan spaces of affine homogeneous spaces

Abstract

Let $G$ be a reductive algebraic group and $H$ its reductive subgroup. Fix a Borel subgroup $B\subset G$ and a maximal torus $T\subset B$. The Cartan space \a_{G,G/H} is, by definition, the subspace of \Lie(T)^* generated by the weights of $B$-semiinvariant rational functions on $G/H$. We compute the spaces \a_{G,G/H}.Comment: v1 20 pages, v2 minor corrections are mad