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For any polynomial representation of the special linear group, the nodes ofthe corresponding crystal may be indexed by semi-standard Young tableaux. Undercertain conditions, the standard Young tableaux occur, and do so with weight 0.Standard Young tableaux also parametrize the vertices of dual equivalencegraphs. Motivated by the underlying representation theory, in this paper, weexplainthis connection by giving a combinatorial manifestation of Schur-Weylduality. In particular, we put a dual equivalence graph structure on the0-weight space of certain crystal graphs, producing edges combinatorially fromthe crystal edges. The construction can be expressed in terms of the localcharacterizations given by Stembridge for crystal graphs and the author fordual equivalence graphs.

A combinatorial realization of Schur-Weyl duality via crystal graphs and dual equivalence graphs