Orbits in the flag variety and images of the moment map for classical groups I

We propose algorithms to get representatives and the images of the moment map of conormal bundles of $GL(p,\mbox{\bf C})\times GL(q,\mbox{\bf C})$-orbits in the flag variety of $GL(p+q,\mbox{\bf C})$, and $GL(p+q,\mbox{\bf C})$-orbits and $Sp(p,\mbox{\bf C})\times Sp(q,\mbox{\bf C})$-orbits in the flag variety of $Sp(p+q,\mbox{\bf C})$ and their signed Young diagrams.