Weyl Modules for the Hyperspecial Current Algebra

We develop the theory of global and local Weyl modules for the hyperspecial current algebra of type A(2n)((2)). We prove that the dimension of a local Weyl module depends only on its highest weight, thus establishing a freeness result for global Weyl modules. Furthermore, we show that the graded local Weyl modules are level one Demazure modules for the corresponding affine Lie algebra. In the last section, we derive the same results for the special current algebras of the twisted affine Lie algebras not of type A(2n)((2)).