The Strong Bernstein-Gelfand-Gelfand Resolution for Generalized Kac-Moody Algebras, I — The Existence of the Resolution

Abstract

The purpose of this series of works is to show the existence of the strong Bernstein-Gelfand-Gelfand resolution (cf. [1]) of the irreducible highest weight module L(A) with dominant integral highest weight A over a symmetrizable generalized Kac-Moody algebra ( = GKM algebra). Here, GKM algebras are a class of contragredient Lie algebras Q(A) over C (see [4], [8], or [7, Chapter 1]) associated to a real square matrix A = (aij)ijel indexed by a finite set / which satisfies the conditions: