Weyl modules for twisted toroidal Lie algebras

In this paper, we extend the notion of Weyl modules for twisted toroidal Lie algebra $\mathcal{T}(\mu )$. We prove that the level one global Weyl modules of $\mathcal{T}(\mu )$ 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 $\mathcal{T}(\mu )$.