Commutative polarisations and the Kostant cascade
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 invarianttheoretic consequences of the existence of a commutative polarisation are also discussed.
 Publication:

arXiv eprints
 Pub Date:
 August 2021
 arXiv:
 arXiv:2108.07750
 Bibcode:
 2021arXiv210807750P
 Keywords:

 Mathematics  Representation Theory;
 Mathematics  Algebraic Geometry;
 17B20;
 17B22;
 17B30
 EPrint:
 22 pages