Journal of Lie Theory

no. 4
Polynomiality for the Poisson Centre of Truncated Maximal Parabolic Subalgebras
Florence Fauquant-Millet1; Polyxeni Lamprou
1Institut Camille Jordan, Université de Lyon, UJM Saint-Etienne, 42023 Saint-Etienne, France
Journal of Lie Theory, Volume 28 (2018) no. 4, pp. 1063-1094
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.
DOI: 10.5802/jolt.1039
Classification: 16W22, 17B22, 17B35
Keywords: Poisson centre, parabolic subalgebras, polynomiality, adapted pairs

Florence Fauquant-Millet  1 ; Polyxeni Lamprou 

1 Institut Camille Jordan, Université de Lyon, UJM Saint-Etienne, 42023 Saint-Etienne, France 
Florence Fauquant-Millet; Polyxeni Lamprou. Polynomiality for the Poisson Centre of Truncated Maximal Parabolic Subalgebras. Journal of Lie Theory, Volume 28 (2018) no. 4, pp. 1063-1094. doi: 10.5802/jolt.1039
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     title = {Polynomiality for the {Poisson} {Centre} of {Truncated} {Maximal} {Parabolic} {Subalgebras}},
     journal = {Journal of Lie Theory},
     pages = {1063--1094},
     year = {2018},
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