3 problems

The covering-polynomial conjecture. The covering polynomial of $\mathfrak{Ad}_0$ satisfies either, equivalently,

Let ${\mathfrak g}$ be a simple Lie algebra, and let ${\mathcal{A}d}({\mathfrak g})$ denote the set of ad-nilpotent ideals of a Borel subalgebra of ${\mathfrak g}$. A duality is an…

Let $G$ be a semisimple algebraic group with Lie algebra ${\mathfrak g}$, and let $\mathfrak{Id}$ denote the set of ad-nilpotent ideals of a fixed Borel subalgebra. For…