Crystal Structure on King Tableaux and Semistandard Oscillating Tableaux
Crystal Structure on King Tableaux and Semistandard Oscillating Tableaux
复制标题
国王画面和半标准振荡画面上的晶体结构
作者：
Seung Jin Lee
在1976年，King（1976）定义了某些tableaux，我们称之为King tableaux，来计算辛群Sp（2 m）的不可约表示的重数。由于晶体被定义，因此在King tableaux上提供晶体结构是一个开放的问题。本文介绍了King表和半标准振荡表的晶体结构。在RSK算法的辛形式中，半标准振荡表自然地表现为Q -表.作为应用，我们给出了Sp（2 m）的Littlewood-Richardson系数的半标准振荡表公式.
In 1976, King (1976) defined certain tableaux, that we call King tableaux, to count weight multiplicities of the irreducible representations of the symplectic group Sp (2 m ). Since crystals are defined, it is an open problem to provide a crystal structure on King tableaux. This paper presents crystal structures on King tableaux and semistandard oscillating tableaux. The semistandard oscillating tableaux naturally appear as Q -tableaux in the symplectic version of RSK algorithms. As an application, we provide a formula for some Littlewood-Richardson coefficients for Sp (2 m ) in terms of semistandard oscillating tableaux.
影响因子：
1
作者：
Lecouvey, Cédric;Lenart, Cristian
通讯作者：
Lenart, Cristian