Mathematics – Representation Theory
Scientific paper
2006-03-22
Mathematics
Representation Theory
16 pages, 7 figures First version used type $B_2$ crystals; current version uses type $C_2$ crystals. To appear in J. Comb. Th
Scientific paper
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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