2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/157910In a recent manuscript, D.Vogan conjectures that four canonical globalizations of Harish-Chandra modules commute with certain n-cohomology groups. In this article we prove that Vogan's conjecture holds for one of the globalizations if and only if it holds for the dual. Using a previously published result of one of the authors, which establishes the conjecture for the minimal globalization, we can therefore deduce Vogan's conjecture for the maximal globalization.A simple proof of the problem raised in arXiv:math/0606071v1Representation TheorySpectral Theory22E46text