Geodesic
Polynomiality for the Poisson Centre of Truncated Maximal Parabolic Subalgebras
Journal of Lie theory, Tome 28 (2018) no. 4, pp. 1063-1094
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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.
Classification : 16W22, 17B22, 17B35
Mots-clés : Poisson centre, parabolic subalgebras, polynomiality, adapted pairs 
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     author = {F. Fauquant-Millet and P. Lamprou},
     title = {Polynomiality for the {Poisson} {Centre} of {Truncated} {Maximal} {Parabolic} {Subalgebras}},
     journal = {Journal of Lie theory},
     pages = {1063--1094},
     year = {2018},
     volume = {28},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JLT_2018_28_4_JLT_2018_28_4_a7/}
}
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F. Fauquant-Millet; P. Lamprou. Polynomiality for the Poisson Centre of Truncated Maximal Parabolic Subalgebras. Journal of Lie theory, Tome 28 (2018) no. 4, pp. 1063-1094. http://geodesic.mathdoc.fr/item/JLT_2018_28_4_JLT_2018_28_4_a7/