Polynomiality for the Poisson Centre of Truncated Maximal Parabolic Subalgebras

Florence Fauquant-Millet (1) , Polyxeni Lamprou (2)

1 AGL - Algèbre, géométrie, logique
2 Weizmann Institute of Science [Rehovot, Israël]

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.

Mots clés: polynomiality; parabolic subalgebras; Poisson centre; adapted pairs

Domaines: Théorie des représentations [math.RT]

Florence Fauquant-Millet, Polyxeni Lamprou. Polynomiality for the Poisson Centre of Truncated Maximal Parabolic Subalgebras. Journal of Lie Theory, 2018, 28 (4), pp.1063-1094. ⟨hal-02002866⟩