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Transformation Groups

, Volume 22, Issue 4, pp 911–932 | Cite as

SLICES FOR MAXIMAL PARABOLIC SUBALGEBRAS OF A SEMISIMPLE LIE ALGEBRA

  • FLORENCE FAUQUANT-MILLET
  • POLYXENI LAMPROUEmail author
Article

Abstract

Let p denote a maximal (truncated) parabolic subalgebra of a simple Lie algebra \( \mathfrak{g} \). It is known that the Poisson centre Y (\( \mathfrak{p} \)) is a polynomial algebra in many cases. We construct a slice for the coadjoint action of p, thus extending a theorem of Kostant. The role of the principal \( \mathfrak{s}\mathfrak{l} \) 2-triple is played by an adapted pair.

AMS Classification 17B35 16W22 

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Université de Lyon UJM-Saint-EtienneSaint-EtienneFrance
  2. 2.Department of MathematicsUniversity of Haifa Mount CarmelHaifaIsrael

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