subregular nilpotent representations of lie algebras in prime ...

30
Lemma: Let J be asabove and let 2 J. Suppose that we have for all 2 F (J)
amodule N( ) in C with dim N( )=h + ; _ ip N ,1 such that T N( ) ' N( )
for all ; 2 F (J). If is subregular, then each N( ) with 2 F (J) is simple.
Proof : Wemay assume that F (J) 6= ;. Then the weight = , + P 2J $
belongs to F (J) since h + ; _ i h + ; _ i