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On the local structure of doubly laced crystals

Philip Sternberg
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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.

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Philip Sternberg. 2006-10-14. On the local structure of doubly laced crystals. https://arxiv.org/abs/math/0603547

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