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arXiv · 2108.07750

Commutative polarisations and the Kostant cascade

Dmitri I. Panyushev
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Abstract

Let $\mathfrak g$ be a complex simple Lie algebra. We classify the parabolic subalgebras $\mathfrak p$ of $\mathfrak g$ such that the nilradical of $\mathfrak p$ has a commutative polarisation. The answer is given in terms of the Kostant cascade. It requires also the notion of an optimal nilradical and some properties of abelian ideals in a Borel subalgebra of $\mathfrak g$. Some invariant-theoretic consequences of the existence of a commutative polarisation are also discussed.

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Dmitri I. Panyushev. 2021-08-17. Commutative polarisations and the Kostant cascade. https://arxiv.org/abs/2108.07750

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