ORBITAL VARIETIES IN SLN AND THE SMITH CONJECTURE

Let O be a nilpotent orbit in the Lie algebra sI(n)(C) (that is, a cla ss of nilpotent elements for conjugation by SLn(C).) Let V be an orbit al variety contained in a and P be the largest parabolic subgroup of S Ln(C) stabilizing V. The Smith conjecture asserts that V contains a de nse P orbit. This is shown to fail in general, and further those nilpo tent orbits for which such a dense orbit exists are determined. (C) 19 98 Academic Press.