Root subgroups on affine spherical varieties

In the study of automorphism groups of toric varieties, a key role is played by one-parameter additive subgroups normalized by the acting torus. Such subgroups are called root subgroups and each of them is uniquely determined by its weight, called the Demazure root of the corresponding toric variety. Moreover, the set of all Demazure roots admits an explicit combinatorial description in terms of the fan defining the toric variety, and this description is especially simple in the case where the variety is affine.
In the setting of arbitrary connected reductive groups acting on algebraic varieties, a natural generalization of toric varieties is given by spherical varieties. A spherical variety is an algebraic variety $X$ equipped with an action of a connected reductive group $G$ in such a way that a Borel subgroup $B \subset G$ has an open orbit in $X$. A proper generalization of root subgroups to spherical varieties is given by $B$-normalized one-parameter additive subgroups, which we call $B$-root subgroups. In the talk we shall discuss $B$-root subgroups on affine spherical varieties, including basic properties, applications, and open problems.
The talk is based on the work http://arxiv.org/abs/2012.02088 joint with I.V. Arzhantsev.