Generalized perfect isometries in some groups of Lie rank one

In a recent paper, B. Külshammer, J.B. Olsson and G.R. Robinson introduced notions of generalized blocks and generalized perfect isometries, and studied them in the case of the symmetric group Sn. It is the purpose of this paper to investigate some families of groups of Lie rank one, exhibiting generalized perfect isometries where there are none in the sense given by M. Broué, and thus proving a (weaker) analogue of one of Brouéʹs conjectures in these cases