UC Riverside

In \cite{CSSW} it was shown that for $\lie{sl_2}$, local Weyl modules have level 2 Demazure flags. In addition, a closed formula was given for the multiplicity of Demazure module in a level 2 Demazure flag. This thesis is a continuation of the work in \cite{CSSW}. More precisely, the objective of this thesis is to develop the framework for constructing level 2 Demazure flags for local Weyl modules for $\lie{sl_n}$. We construct right exact sequences that will (provided they are exact) allow one to construct the level 2 Demazure flag and employ combinatorics to calculate multiplicities of Demazure modules in the flag. In the case of $\lie{sl_3}$ we show that these right exact sequences are exact and give a closed formula for the multiplicities.