论文标题
图表中的痕迹代数I：自由分区量子组，随机晶格路径和在树上随机行走
Traces On Diagram Algebras I: Free Partition Quantum Groups, Random Lattice Paths And Random Walks On Trees
论文作者
论文摘要
我们将极端轨迹分类为由Banica-Speicher的自由分区量子组（ARXIV：0808.2628）和Weber（Arxiv：Arxiv：1201.4723）分类而产生的非交叉分区的七个直接限制代数。对于无限维temperley-lieb-algebra（对应于量子组$ o^+_ n $）和motzkin代数（$ b^+_ n $），极端痕迹的分类意味着针对众所周知的中央随机晶格路径类型的分类结果。对于$ 2 $ -FUSS-CATALAN代数（$ H_n^+$），我们通过计算\ emph {\ emph {minimal或退出边界}（也称为\ emph {absolute}）来解决分类问题，以在fibonacci树上进行中心随机步行，从而解决fibonacci树，从而解决一个概率的独立问题，并以我们的知识为基础，并以我们的知识为基础，从而解决了一个不明显的知识。在本文的过程中，我们还讨论了所有自由分区量子组的七个示例的分支图，计算尚未知道的量子组，并为其不可约表示的维度提供新的公式。
We classify extremal traces on the seven direct limit algebras of noncrossing partitions arising from the classification of free partition quantum groups of Banica-Speicher (arXiv:0808.2628) and Weber (arXiv:1201.4723). For the infinite-dimensional Temperley-Lieb-algebra (corresponding to the quantum group $O^+_N$) and the Motzkin algebra ($B^+_N$), the classification of extremal traces implies a classification result for well-known types of central random lattice paths. For the $2$-Fuss-Catalan algebra ($H_N^+$) we solve the classification problem by computing the \emph{minimal or exit boundary} (also known as the \emph{absolute}) for central random walks on the Fibonacci tree, thereby solving a probabilistic problem of independent interest, and to our knowledge the first such result for a nonhomogeneous tree. In the course of this article, we also discuss the branching graphs for all seven examples of free partition quantum groups, compute those that were not already known, and provide new formulas for the dimensions of their irreducible representations.
