REPRESENTATIONS OF GRADED MULTILOOP LIE ALGEBRAS

Let (g) over tilde (A) (respectively, (g) over tilde (A) (mu)) be the graded multiloop Lie algebra (respectively, graded twisted multiloop Lie algebra) associated with the simple finite dimensional Lie algebra g over C. In this article, we prove that irreducible integrable (g) over tilde (A) (mu)-modules with finite dimensional weight spaces are either highest weight modules or their duals and classify the isomorphism classes of irreducible integrable (g) over tilde (A)-modules and (g) over tilde (A)(mu)-modules with finite dimensional weight spaces.