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Journal of Lie Theory 28 (2018), No. 4, 1063--1094
Copyright Heldermann Verlag 2018

Polynomiality for the Poisson Centre of Truncated Maximal Parabolic Subalgebras

Florence Fauquant-Millet
Institut Camille Jordan, Université de Lyon, UJM Saint-Etienne, 42023 Saint-Etienne, France

Polyxeni Lamprou

We study the Poisson centre of truncated maximal parabolic subalgebras of a simple Lie algebra of type B, D or E6. 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

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