Adapted pairs in type $A$ and regular nilpotent elements

Florence Fauquant-Millet, Anthony Joseph

Let $\mathfrak{g}$ be a simple Lie algebra over an algebraically closed field $\mathbf{k}$ of characteristic zero and $\mathbf{G}$ its adjoint group. Let $\mathfrak{q}$ be a biparabolic subalg…