Slices for maximal parabolic subalgebras of a semisimple Lie algebra
Abstract
Let p be a maximal truncated parabolic subalgebra of a simple Lie Algebra. It was shown in many cases that the Poisson centre Y(p) is a polynomial algebra. We construct a slice for the coadjoint action of p, thus extending a theorem of Kostant. The role of the principal sl2-triple is played by an adapted pair.
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