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As in the case of Mumford's geometric invariant theory (which concerns projective good quotients) the problem can be reduced to the case of an action of a torus.
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We also show how to distinguish examples of open subsets with a good quotient coming from Mumford's theory and give examples of open subsets with non-quasi-projective quotients.
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Cones of highest weight vectors, weight polytopes, and Lusztig's q-analog
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As an application of the results we prove a generalization of Chevalley's restriction theorem for the classical Lie algebras.
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Let g be a Lie algebra,S(g) the symmetric algebra,U(g) the universal enveloping algebra, andZ(g) the center ofU(g).
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