  The right key of a semistandard Young tableau is a tool used to find Demazure
characters for $sl_n(\mathbb{C})$. This thesis gives methods to obtain the
right and left keys by inspection of the semistandard Young tableau. Given a
partition $\lambda$ and a Weyl group element $w$, there is a semistandard Young
tableau $Y_\lambda(w)$ of shape $\lambda$ that corresponds to $w$. The Demazure
character for $\lambda$ and $w$ is known to be the sum of the weights of all
tableaux whose right key is dominated by $Y_\lambda(w)$. The set of all such
tableaux is denoted $\mathcal{D}_\lambda(w)$. Exploiting the method mentioned
above for obtaining right keys, this thesis describes the entry at each
location in any $T \in \mathcal{D}_\lambda(w)$. Lastly, we will consider
$\mathcal{D}_\lambda(w)$ as an integral subset of Euclidean space. The final
results present a condition that is both necessary and sufficient for this
subset to be convex.
