On the Hypersurface Orbital Varieties of sl(N, )

We study the structure of hypersurface orbital varieties of sl(N, ) (those that are hypersurfaces in the nilradical of some parabolic subalgebra) and how information about this structure is encoded in the standard Young tableau associated to it by the Robinson–Schensted algorithm. We present a conjecture for the exact form of the unique non-linear defining equations of hypersurface orbital varieties and proofs of the conjecture in certain cases.