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) x C-x 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.

On some families of smooth affine spherical varieties of full rank / Paulus, Kay; Pezzini, Guido; Van Steirteghem, Bart. - In: ACTA MATHEMATICA SINICA. - ISSN 1439-8516. - STAMPA. - 34:3(2018), pp. 563-596.

On some families of smooth affine spherical varieties of full rank

Guido Pezzini;
2018

Abstract

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) x C-x 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.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11573/1026258
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