Abstract
Let $\mathfrak{g}$ be a Lie algebra all of whose regular subalgebras of rank 2 are
type $A_{1}\times A_{1}$, $A_{2}$, or $C_{2}$, and let $B$ be a crystal graph corresponding
to a representation of $\mathfrak{g}$. We explicitly describe the local structure of $B$,
confirming a conjecture of Stembridge.
