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arXiv · 1710.09622

A local characterization of $B_2$ regular crystals

Shunsuke Tsuchioka
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Abstract

Stembridge characterized regular crystals associated with a simply-laced generalized Cartan matrix (GCM) in terms of local graph-theoretic quantities. We give a similar axiomatization for $B_2$ regular crystals and thus for regular crystals associated with a finite GCM except $G_2$ and an affine GCM except $A^{(1)}_{1},G^{(1)}_{2},A^{(2)}_{2},D^{(3)}_4$.

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Shunsuke Tsuchioka. 2017-10-26. A local characterization of $B_2$ regular crystals. https://arxiv.org/abs/1710.09622

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