Abstract
In this paper we relate the deformation method in invariant theory to spherical subgroups. Let G be a reductive group, Z an affine G-variety and H⊂G a spherical subgroup. We show that whenever G/H is affine and its semigroup of weights is saturated, the algebra of H-invariant regular functions on Z has a G-invariant filtration such that the associated graded algebra is the algebra of regular functions of some explicit horospherical subgroup of G. The deformation method in its usual form, as developed by Luna et al., is a particular case of this construction. Our result also applies to the description of invariants of some reducible representations of reductive groups.
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