{"title":"A local characterization of $B_{2}$ regular crystals","authors":"Shunsuke Tsuchioka","doi":"10.3792/pjaa.97.010","DOIUrl":null,"url":null,"abstract":"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.","PeriodicalId":49668,"journal":{"name":"Proceedings of the Japan Academy Series A-Mathematical Sciences","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2017-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the Japan Academy Series A-Mathematical Sciences","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3792/pjaa.97.010","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 2
Abstract
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.
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。
期刊介绍：
The aim of the Proceedings of the Japan Academy, Series A, is the rapid publication of original papers in mathematical sciences. The paper should be written in English or French (preferably in English), and at most 6 pages long when published. A paper that is a résumé or an announcement (i.e. one whose details are to be published elsewhere) can also be submitted.
The paper is published promptly if once communicated by a Member of the Academy at its General Meeting, which is held monthly except in July and in August.
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