UC Riverside

In this thesis, I study certain generalized Demazure modules for a twisted current algebra of type $^2\tilde{A}_{2\ell-1}$; that is, the fixed point subalgebra under an order 2 graph \newline automorphism defined on an untwisted affine Lie algebra of type $\tilde{A}_{2\ell-1}$. In particular, I give a presentation of a family of generalized Demazure modules which can be realized as a submodule of the tensor product of two level one Demazure modules. I also show that, in certain cases, this type of generalized Demazure module is in fact isomorphic to a level two Demazure module.