Orbital Varieties in imageimageNand the Smith Conjecture

Let image be a nilpotent orbit in the Lie algebra imageimagen(image) (that is, a class of nilpotent elements for conjugation bySLn(image).) Let image be an orbital variety contained in image andPbe the largest parabolic subgroup ofSLn(image) stabilizing image. The Smith conjecture asserts that image contains a densePorbit. This is shown to fail in general, and further those nilpotent orbits for which such a dense orbit exists are determined.