UC Riverside

In recent work published by Biswal, Chari, Shereen, and Wand the authors defined a family of symmetric polynomials indexed by pairs of dominant integral weights, G_{\nu, \lambda}(z,q) where z=(z_1, \cdots. z_{n+1})\in\C^{n+1}, and determined that G_{0, \lambda}(z,q) is the graded character of a level two Demazure module for sl_{n+1}[t]. The aim of this thesis is to construct analogues of these polynomials for the generalized Demazure modules for so_{2n}[t] as they are presented by Chari, Davis, and Moruzzi. We do this by constructing modules which interpolate from the presentation provided in that paper and local Weyl modules. We then create short exact sequences between them to relate their graded characters. This allows us to identify coefficients in the corresponding graded characters with the coefficients in G_{\nu,\lambda}(z,q).