2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63525We define a partial order on the set of pairs {(O,C)}, where O is a nilpotent orbit and C is a conjugacy class in Lusztig's canonical quotient of A(O). We then show that there is a unique order-reversing duality map on this set that has certain properties analagous to those of the original Lusztig-Spaltenstein duality map. This generalizes work of E. Sommers. In this revised version, a new approach leads to a strengthened version of Theorem 2, and applications of the results are discussed in greater detail.27 pages; corrected attributions of earlier work in the last sectionRepresentation Theorytext