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On deformation method in invariant theory

Dmitri Panyushev (1997)

Annales de l'institut Fourier

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...

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