2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/110294Let $\mathfrak{g}$ 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.16 pages, 7 figures First version used type $B_2$ crystals; current version uses type $C_2$ crystals. To appear in J. Comb. Theory, Ser. ARepresentation TheoryCombinatorics17B37 (Primary) 05C75 (Secondary)text