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Let G be a complex reductive algebraic group. Fix a Borel subgroup B of G and a maximal torus T in B. Call the monoid of dominant weights L+ and let S be a finitely generated submonoid of L+. V. Alexeev and M. Brion introduced a moduli scheme MS which classifies affine G-varieties X equipped with a T-equivariant isomorphism SpecC[X]U → SpecC[S], where U is the unipotent radical of B. Examples of MS have been obtained by S. Jansou, P. Bravi and S. Cupit-Foutou. In this paper, we prove that MS is isomorphic to an affine space when S is the weight monoid of a spherical G-module with G of type A. Unlike the earlier examples, this includes cases where S does not satisfy the condition hSiZ ∩ L+ = S.


This article originally appeared in Annales de l'institut Fourier, available at DOI: 10.5802/aif.2735

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