$B_{2}$正则晶体的局部表征

Pub Date : 2017-10-26 DOI:10.3792/pjaa.97.010

Shunsuke Tsuchioka

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引用次数: 2

摘要

Stembridge用局部图论量描述了与简单带状GCM相关的规则晶体。对于$B_2$规则晶体，我们给出了类似的公理化(因此对于除$G_2$外的有限GCM的规则晶体和除$ a ^{(1)}_{1}，G^{(1)}_{2}， a ^{(2)}_{2}，D^{(3)}_4$外的仿射GCM)。我们的动机来自于作者与渡边雅明共同对Schur分拆定理的推广，并通过完美晶体理论间接证明。

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A local characterization of $B_{2}$ regular crystals

Stembridge characterizes regular crystals associated with a simply-laced GCM in terms of local graph-theoretic quantities. We give a similar axiomatization for $B_2$ regular crystals (and thus for regular crystals of finite GCM except $G_2$ and affine GCM except $A^{(1)}_{1},G^{(1)}_{2},A^{(2)}_{2},D^{(3)}_4$). Our motivation comes from a generalization of Schur partition theorem by the author jointly with Masaki Watanabe proved indirectly via theory of perfect crystal.

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