Verma module imbeddings and the Bruhat order for Kac-Moody algebras (Q1090406)

The author discusses the connection between the Bruhat order on the Weyl group and Verma module embedding in the case of a Kac-Moody Lie algebra \({\mathfrak g}\). \({\mathfrak g}\) is defined here by a (not necessarily symmetrizable) generalized Cartan matrix. It is proved that if both highest weights of Verma modules are in the same Weyl group orbit of a dominant integral weight, then the existence of imbeddings is determined by the Bruhat order on the Weyl group.