Rook placements in $G_2$ and $F_4$ and associated coadjoint orbits

Mikhail V. Ignatev, Matvey A. Surkov

Let $\mathfrak{n}$ be a maximal nilpotent subalgebra of a simple complex Lie algebra with root system $\Phi$. A subset $D$ of the set ${\Phi }^{+}$ of positive roots is called a rook placemen…