Slices for maximal parabolic subalgebras of a semisimple Lie algebra

Published 11 Nov 2015 in math.RT | (1511.03542v1)

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 sl_2-triple is played by an adapted pair.

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