A unified formula for Steenrod operations in flag manifolds

The classical Schubert cells on a flag manifold $G/P$ give a cell decomposition for $G/P$ whose Kronecker duals (known as Schubert classes) form an additive base for the integral cohomology $H^{\ast}(G/P)$. We present a formula that expresses Steenrod mod-$p$ operations on Schubert classes in $G/P$ in terms of Cartan numbers of $G$.