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Affine open orbits, reductive isotropy groups, and dominant gradient morphisms; a theorem of Mikio Sato
An algebraic proof is given for a theorem of M. Sato.The theorem gives criteria for the open orbit in a prehomogeneous vector space under a reductive group to be an affine variety.The following conditions are equivalent:1. 0(G) the open orbit is an affine variety. G z the isotropy subgroup of …