Some remarks on the uniqueness of liftings of principal indecomposable modules for infinitesimal subgroups of semisimple groups

This note is in the nature of an appendix to the recent paper by Paul Sobaje, [5]. In that paper, Section 2.2 the question of the uniqueness of G structures on (or liftings of) principal indecomposable G1-module in the case G=SL3 is raised. We here answer this question positively as well as making some more general observations.