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

Abstract

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 an open G-orbit by means of a suitable B-normalized one-parameter additive action.