论文标题
苏克氏仙人掌，虚拟化和贝伦斯坦 - 基里洛夫组
Symplectic cacti, virtualization and Berenstein-Kirillov groups
论文作者
论文摘要
我们明确地意识到了符合仙人掌群的内部作用，该组最近由哈拉切瓦（Halacheva）定义为任何复杂，还原性，有限的，有限的利用代数，对kashiwara-nakashima tableaux的晶体。我们的方法包括由于悬挂式和贝克（Baker）引起的虚拟化和虚拟化而导致的jeu de taquin的符合版本。作为应用程序，我们定义并研究了Berenstein-Kirillov组的符合性版本，并表明它是Symblectic Cactus组的商。此外，还给出了同骨berenstein-kirillov群体的两个关系，这些关系并不遵循同成立仙人掌群的定义关系。
We explicitly realize an internal action of the symplectic cactus group, recently defined by Halacheva for any complex, reductive, finite-dimensional Lie algebra, on crystals of Kashiwara-Nakashima tableaux. Our methods include a symplectic version of jeu de taquin due to Sheats and Lecouvey, symplectic reversal, and virtualization due to Baker. As an application, we define and study a symplectic version of the Berenstein-Kirillov group and show that it is a quotient of the symplectic cactus group. In addition two relations for symplectic Berenstein-Kirillov group are given that do not follow from the defining relations of the symplectic cactus group.
