标题： 关于与半单李代数晶体相关的高秩图的一些结果 显示英文标题

标题： Some results on the higher-rank graphs associated to crystals of semisimple Lie algebras

摘要： 本文中，我们继续研究作者与R. Yuncken引入的与有限维复半单李代数相关的高秩图，其构造依赖于柏原理论中的晶体理论。 首先我们证明了相应外尔群的Bruhat图（无论是弱型还是强型）都可以作为带颜色的图嵌入到高秩图中。 接着，我们将研究对象专门化为类型为$A$的李代数，将高秩图构造的一些方面与组合数学中一些著名的概念联系起来，最引人注目的是Lascoux和Schützenberger的键。 显示英文摘要

摘要： In this paper we continue the study of the higher-rank graphs associated to finite-dimensional complex semisimple Lie algebras, introduced by the author and R. Yuncken, whose construction relies on Kashiwara's theory of crystals. First we prove that the Bruhat graphs of the corresponding Weyl groups, both weak and strong, can be embedded into the higher-rank graphs as colored graphs. Next, specializing to Lie algebras of type $A$, we connect some aspects of the construction of the higher-rank graphs with some well-known notions in combinatorics, most notably the keys of Lascoux and Sch\"utzenberger.