Roman Avdeev

Let G be a connected semisimple algebraic group, H a connected reductive
subgroup of G, and X = G/P a flag variety. According to a result of Vinberg
and Kimelfeld from 1978, the following conditions are equivalent:
(1) the natural action of H on X is spherical (that is, a Borel subgroup of
H has an open orbit in X);
(2) for every irreducible representation R of G realized in the space of
sections of a homogeneous line bundle on X, the restriction of R to H is
multiplicity free.
Under conditions (1) and (2) the restrictions to H of all such irreducible
representations of G are described by a free monoid of finite rank, called
the branching monoid.
In the talk, we shall discuss how to classify all triples (G,H,X)
satisfying (1) and (2) and how to compute the corresponding branching
monoids for them.
This is a joint project with Alexey Petukhov.