
Journal of Lie Theory 28 (2018), No. 4, 10631094 Copyright Heldermann Verlag 2018 Polynomiality for the Poisson Centre of Truncated Maximal Parabolic Subalgebras Florence FauquantMillet Institut Camille Jordan, Université de Lyon, UJM SaintEtienne, 42023 SaintEtienne, France florence.millet@univstetienne.fr Polyxeni Lamprou polyxeni.lamprou@googlemail.com We study the Poisson centre of truncated maximal parabolic subalgebras of a simple Lie algebra of type B, D or E_{6}. In particular we show that this centre is a polynomial algebra and compute the degrees of its generators. In roughly half of the cases the polynomiality of the Poisson centre was already known by a completely different method. For the rest of the cases, our approach is to construct an algebraic slice in the sense of Kostant given by an adapted pair and the computation of an improved upper bound for the Poisson centre. Keywords: Poisson centre, parabolic subalgebras, polynomiality, adapted pairs. MSC: 16W22, 17B22, 17B35 [ Fulltextpdf (244 KB)] for subscribers only. 