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In this paper, we extend the notion of Weyl modules for twisted toroidal Lie algebra T (). We prove that the level one global Weyl modules of T () are isomorphic to the tensor product of the level one representation of twisted affine Lie algebras and certain lattice vertex algebras. As a byproduct, we calculate the graded character of the level one local Weyl modules of T ().
Pandey et al. (Sat,) studied this question.