Integrable Modules For Graded Lie Tori With Finite Dimensional Weight Spaces

Abstract: An important problem in the representation theory of affine and toroidal Lie algebras is to classify all possible irreducible integrable modules with finite dimensional weight spaces. Recently the irreducible integrable modules having finite dimensional weight spaces with non-trivial central action have been classified for a more general class of Lie algebras, namely the graded Lie tori. In this paper, we classify all the irreducible integrable modules with finite dimensional weight spaces for this graded Lie tori where the central elements act trivially. Thus we ultimately obtain all the simple objects in the category of integrable modules with finite dimensional weight spaces for the graded Lie tori.