Solvable spherical subgroups and their combinatorial invariants

In a recent paper, the speaker developed a structure theory of
connected solvable spherical subgroups in semisimple algebraic groups.
The aim of the talk is to demonstrate applications of this theory to
computation of several combinatorial invariants of spherical
homogeneous spaces corresponding to the subgroups in consideration.
The first of the invariants is the so-called extended weight semigroup
of a homogeneous space. In our situation, this semigroup carries a lot
of information that allows one to compute other invariants attached to
a spherical homogeneous space such as weight lattice, spherical roots,
and colors.