ON EXTENDED WEIGHT MONOIDS OF SPHERICAL HOMOGENEOUS SPACES

Given a connected reductive complex algebraic group $G$ and spherical subgroup $H \subset G$, the extended weight monoid $\widehat \Lambda^+_G(G/H)$ encodes $G$-module structures on spaces of global sections all $G$-linearized line bundles $G/H$. Assuming that is semisimple simply $H$ specified by regular embedding in parabolic $P this paper we obtain description via set simple roots $G/H$ together with certain combinatorial data explicitly computed from pair $(P,H)$. As an application, deduce new proof result Avdeev Gorfinkel describing case where strongly solvable.