On the Existence of B-Root Subgroups on Affine Spherical Varieties

Let X be an irreducible affine algebraic variety that is spherical with respect to action of a connected reductive group G. In this paper, we provide sufficient conditions, formulated in terms weight combinatorics, for the existence one-parameter additive actions on $$X$$ normalized by Borel subgroup $$B \subset G$$ . As application, prove every G-stable prime divisor can open G-orbit means suitable B-normalized action.