In this paper, we show that a K a c M o o d y algebra fl(A) associated to a symmetr izable generalized Car tan matr ix A carries a cont ravar ian t Hermi t i an form which is positive-definite on all root spaces. We deduce that every integrable highest weight g(A)-module L(A) carries a cont ravar ian t positivedefinite Hermi t i an form. This allows us to… (More)