Let G be a complex connected reductive group. Losev has shown that a smooth affine spherical G-variety X is uniquely determined by its weight monoid, which is the set of irreducible representations of G that occur in ...Let G be a complex connected reductive group. Losev has shown that a smooth affine spherical G-variety X is uniquely determined by its weight monoid, which is the set of irreducible representations of G that occur in the coordinate ring of X. In this paper we use a combinatorial characterization of the weight monoids of smooth affine spherical varieties to classify：（a） all such varieties for G = SL（2） × C~×and（b） all such varieties for G simple which have a G-saturated weight monoid of full rank. We also use the characterization and Knop＇s classification theorem for multiplicity free Hamiltonian manifolds to give a new proof of Woodward＇s result that every reflective Delzant polytope is the moment polytope of such a manifold.展开更多
基金partially supported by the DFG Schwerpunktprogramm 1388–Darstellungstheoriesupport from the National Science Foundation(USA)through grant DMS 1407394the PSC-CUNY Research Award Program
文摘Let G be a complex connected reductive group. Losev has shown that a smooth affine spherical G-variety X is uniquely determined by its weight monoid, which is the set of irreducible representations of G that occur in the coordinate ring of X. In this paper we use a combinatorial characterization of the weight monoids of smooth affine spherical varieties to classify：（a） all such varieties for G = SL（2） × C~×and（b） all such varieties for G simple which have a G-saturated weight monoid of full rank. We also use the characterization and Knop＇s classification theorem for multiplicity free Hamiltonian manifolds to give a new proof of Woodward＇s result that every reflective Delzant polytope is the moment polytope of such a manifold.
