Polynomiality for the Poisson Centre of Truncated Maximal Parabolic Subalgebras

F. Fauquant-Millet; P. Lamprou

doi:10.5802/jolt.1039

F. Fauquant-Millet; P. Lamprou

Journal of Lie Theory, Volume 28 (2018) no. 4, pp. 1063-1094

Abstract

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.

arXiv Zbl

DOI: 10.5802/jolt.1039

Classification: 16W22, 17B22, 17B35
Keywords: Poisson centre, parabolic subalgebras, polynomiality, adapted pairs

@article{JOLT_2018_28_4_a7,
     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},
     doi = {10.5802/jolt.1039},
     zbl = {1452.17015},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1039/}
}

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F. Fauquant-Millet; P. 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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