论文标题
Gelfand-Tsetlin晶体
Gelfand-Tsetlin Crystals
论文作者
论文摘要
我们在Gelfand-tsetlin模式的集合上给出了一个晶体结构，该模式为一般线性lie代数的有限维不可减少表示的碱基化。晶体数据以封闭形式给出，使用模式条目的热带多项式函数表示。我们证明，使用这种晶体结构，Gelfand-Tsetlin模式与Semistandard Young Tableaux之间的自然培养是一种晶体同构。
We give a crystal structure on the set of Gelfand-Tsetlin patterns which parametrize bases for finite-dimensional irreducible representations of the general linear Lie algebra. The crystal data are given in closed form, expressed using tropical polynomial functions of the entries of the patterns. We prove that with this crystal structure, the natural bijection between Gelfand-Tsetlin patterns and semistandard Young tableaux is a crystal isomorphism.
