论文标题
图表代数II：易于组的中央代数和年轻图的新变体
Traces on diagram algebras II: Centralizer algebras of easy groups and new variations of the Young graph
论文作者
论文摘要
在我们最近的作品（2006.07312）的持续延续中，我们对Banica和Speicher轻松群体的Schur-Weyl二元性的无限图代数上的极端痕迹进行了分类。我们表明，这些代数的分支图描述了年轻图的新变化的步行，这些变化描述了奇怪的年轻图表。结果，我们证明，通用的Rook-brauer代数上的极端痕迹始终是Infinite对称组的组代数$ \ Mathbb {c} [s _ {\ infty}] $的极端痕迹。此外，我们猜测，对于高核群的中心化的通用参数变形也是如此，我们将此猜想减少到概念上更简单的数值语句。最后，我们解决了半流动正交组$ o_n^*$的痕量分类问题，在这种情况下，极端痕迹始终是$ \ mathbb {c} [c} [s _ {\ infty} \ times s _ {s _ {\ infty}] $ \ mathbb {c}上的极端痕迹。我们的方法取决于Vershik和Nikitin开发的方法。
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.
