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arXiv · 2309.14898

A local characterization of quasi-crystal graphs

Alan J. Cain·António Malheiro·Fátima Rodrigues·Inês Rodrigues
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Abstract

It is provided a local characterization of quasi-crystal graphs, by presenting a set of local axioms, similar to the ones introduced by Stembridge for crystal graphs of simply-laced root systems. It is also shown that quasi-crystal graphs satisfying these axioms are closed under the tensor product recently introduced by Cain, Guilherme and Malheiro. It is deduced that each connected component of such a graph has a unique highest weight element, whose weight is a composition, and it is isomorphic to a quasi-crystal graph of semistandard quasi-ribbon tableaux.

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Alan J. Cain, António Malheiro, Fátima Rodrigues, Inês Rodrigues. 2023-09-26. A local characterization of quasi-crystal graphs. https://arxiv.org/abs/2309.14898

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