图代数II的迹：易群的中心化子代数和Young图的新变种
Traces on diagram algebras II: Centralizer algebras of easy groups and new variations of the Young graph
摘要：
在我们最近的工作arXiv：2006.07312的延续，我们分类的极值轨迹上的无限图代数的Schur-Weyl对偶的Banica和Speicher的容易群的上下文中出现的。我们表明，这些代数的分支图描述走在新的变化的杨图描述好奇的方式不断增长的杨图。证明了一般rook-Brauer代数上的极迹总是无限对称群的群代数$\mathbb{C}[S_{\infty}]$上的极迹的扩张.此外，我们猜想，同样是真实的通用参数变形的超八面体群的中心化，我们减少了这个猜想到一个概念上更简单的数值语句。最后，我们解决的Schur-Weyl对偶的半解放正交群$O_N^*$，在这种情况下，极值迹总是极值迹$\mathbb{C}[S_{\infty} \times S_{\infty}]$上的扩展的跟踪分类问题。我们的方法依赖于Vershik和Nikitin开发的方法。
英文摘要：
In continuation of our recent work arXiv:2006.07312, we classify the extremal traces on infinite diagram algebras that appear in the context of Schur-Weyl duality for Banica and Speicher's easy groups. We show that the branching graphs of these algebras describe walks on new variations of the Young graph which describe curious ways of growing Young diagrams. As a consequence, we prove that the extremal traces on generic rook-Brauer algebras are always extensions of extremal traces on the group algebra $\mathbb{C}[S_{\infty}]$ of the infinite symmetric group. Moreover, we conjecture that the same is true for generic parameter deformations of the centralizers of the hyperoctahedral group and we reduce this conjecture to a conceptually much simpler numerical statement. Lastly, we address the trace classification problem for the Schur-Weyl dual of the halfliberated orthogonal group $O_N^*$, in which case extremal traces are always extensions of extremal traces on $\mathbb{C}[S_{\infty} \times S_{\infty}]$. Our approach relies on methods developed by Vershik and Nikitin.
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