Geodesic
The Frobenius semiradical, generic stabilizers, and Poisson center for nilradicals
Canadian journal of mathematics, Tome 76 (2024) no. 6, pp. 2019-2048

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DOI

Let ${\mathfrak g}$ be a complex simple Lie algebra and ${\mathfrak n}$ the nilradical of a parabolic subalgebra of ${\mathfrak g}$. We consider some properties of the coadjoint representation of ${\mathfrak n}$ and related algebras of invariants. This includes (i) the problem of existence of generic stabilizers, (ii) a description of the Frobenius semiradical of ${\mathfrak n}$ and the Poisson center of the symmetric algebra , (iii) the structure of as -module, and (iv) the description of square integrable (= quasi-reductive) nilradicals. Our main technical tools are the Kostant cascade in the set of positive roots of ${\mathfrak g}$ and the notion of optimization of ${\mathfrak n}$.
DOI : 10.4153/S0008414X23000718
Mots-clés : Coadjoint action, Kostant cascade, Frobenius semiradical, Poisson center 
Panyushev, Dmitri I. The Frobenius semiradical, generic stabilizers, and Poisson center for nilradicals. Canadian journal of mathematics, Tome 76 (2024) no. 6, pp. 2019-2048. doi: 10.4153/S0008414X23000718
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     title = {The {Frobenius} semiradical, generic stabilizers, and {Poisson} center for nilradicals},
     journal = {Canadian journal of mathematics},
     pages = {2019--2048},
     year = {2024},
     volume = {76},
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     doi = {10.4153/S0008414X23000718},
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