On Some Families of Smooth Affine Spherical Varieties of Full Rank

作     者：Kay PAULUS Guido PEZZINI Bart VAN STEIRTEGHEM 

作者机构：Department Mathematik FA U Erlangen-Niirnberg 91058 Erlangen Germany Dipartimento di Matematica 'Sapienza' Universith di Roma 00185 Roma Italy Department Mathematik FA U Erlangen-Niirnberg & Department of MathematicsMedgar Evers College-City University of New York Brooklyn New York 11225 USA 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2018年第34卷第3期

页      面：563-596页

核心收录：

学科分类：07[理学] 

基　　金：partially supported by the DFG Schwerpunktprogramm 1388–Darstellungstheorie support from the National Science Foundation(USA)through grant DMS 1407394 the PSC-CUNY Research Award Program 

主　　题：Affine spherical variety weight monoid multiplicity free Hamiltonian manifold moment polytope 

摘      要：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.