Combinatorial characterization of the weight monoids of smooth affine spherical varieties

Abstract

Let G G be a connected reductive group, and let X X be a smooth affine spherical G G -variety, both defined over the complex numbers. A well-known theorem of I. Losev’s says that X X is uniquely determined by its weight monoid, which is the set of irreducible representations of G G that occur in the coordinate ring of X X . In this paper, we use the combinatorial theory of spherical varieties and a smoothness criterion of R. Camus to characterize the weight monoids of smooth affine spherical varieties.