No CrossRef data available.
Article contents
The Frobenius semiradical, generic stabilizers, and Poisson center for nilradicals
Published online by Cambridge University Press: 27 October 2023
Abstract
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 ${\mathfrak n}$.
- Type
- Article
- Information
- Copyright
- © The Author(s), 2023. Published by Cambridge University Press on behalf of The Canadian Mathematical Society