{"title":"$B_{2}$正则晶体的局部表征","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":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2017-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"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\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2017-10-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.3792/pjaa.97.010\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3792/pjaa.97.010","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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。
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.