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