Borel subalgebras and categories of highest weight modules for toroidal Lie algebras

In this article we begin an investigation of the conjugacy classes of Borel subalgebras together with Verma modules induced from "standard" Borel suba lgebras of a toroidal Lie algebra t in mio variables. We define, for each h ighest weight lambda, a category @(lambda) of representations of t that con tain these Verma modules and show that when a certain central element acts nontrivially this category is equivalent to the category @(lambda)((m) over cap) for an extension of a suitable affine Kac-Moody algebra (m) over cap subset of t. From this equivalence we obtain a EGG type resolution and EGG duality theorem in the setting of @(lambda). (C) 2001 Academic Press.