  We study representations of the Loop Kac-Moody Lie algebra g \otimes A, where
g is any Kac-Moody algebra and A is a ring of Laurent polynomials in n
commuting variables. In particular, we study representations with finite
dimensional weight spaces and their graded versions. When we specialize g to be
a finite dimensional or affine Lie algebra we obtain modules for toroidal Lie
algebras.

Representation Theory