Projections of singular vectors of Verma modules over rank 2 Kac-Moody Lie algebras

We begin with a brief historical overview and provide motivation for the significance of what follows. In the second chapter we introduce relevant definitions and concepts in the course of providing some details missing in the proof of Kac and Kazhdan's celebrated criterion for the irreducibility of Verma modules over Kac-Moody Lie algebras. In the third chapter we generalize work of Fuchs concerning projections of singular vectors of Verma modules over Kac-Moody algebras. The original result gave fomulas for the Lie algebra A1 1 . Here we expand the result to the entire family of rank two Kac-Moody Lie algebras.