Rook placements in $A_n$ and combinatorics of $B$-orbit closures

Mikhail V. Ignatyev, Anton S. Vasyukhin

Let $G$ be a complex reductive group, $B$ be a Borel subgroup of G, $\nt$ be the Lie algebra of the unipotent radical of $B$, and $\nt^*$ be its dual space. Let $\Phi$ be the root sys…