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.
Papadakis, Stavros Argyrios and Steirteghem, Bart Van, "EQUIVARIANT DEGENERATIONS OF SPHERICAL MODULES FOR GROUPS OF TYPE A" (2012). CUNY Academic Works.