Generalized perfect isometries in some groups of Lie rank one

Jean-Baptiste Gramain

In a recent paper, B. K\"ulshammer, J. B. Olsson and G. R. Robinson
introduced notions of {\em generalized blocks\/} and {\em generalized
perfect isometries}, and studied them in the case of the symmetric
group $S_n$. 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. Brou\'e, 
and thus proving a (weaker) analogue of one of Brou\'e\s Conjectures
in these cases.