SLICES FOR MAXIMAL PARABOLIC SUBALGEBRAS OF A SEMISIMPLE LIE ALGEBRAReportar como inadecuado




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1 ICJ - Institut Camille Jordan Villeurbanne 2 WIS - Weizmann Institute of Science

Abstract : Let p denote a maximal truncated parabolic subalgebra of a simple Lie algebra g. In F. Fauquant-Millet and A. Joseph, Semi-centre de l-alg ebre en-veloppante d-une sous-alg ebre parabolique d-une alg ebre de Lie semi-simple, Ann. Sci. Ecole. Norm. Sup. 4 38 2005 no.2, 155-191 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, a notion introduced in A. Joseph and P. Lamprou, Maximal Poisson commutative subalgebras for truncated para-bolic subalgebras of maximal index in sl n , Transform. Groups 12 2007, no. 3, 549-571.

Keywords : Poisson Centre Truncated Parabolic Subalgebras Slices





Autor: Florence Fauquant-Millet - Polyxeni Lamprou -

Fuente: https://hal.archives-ouvertes.fr/



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