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