Remark on nilpotent orbits

If $G$ is a reductive Lie group and ${\mathcal{O}_f} = \operatorname{Ad} {(G)^ \ast }f$ is a nilpotent coadjoint orbit with invariant real polarization $\mathfrak{p}$, then ${\mathcal{O}_f}$ is identified as an open $G$-orbit on the cotangent bundle of $G/P$.