环面与无限块对角对称群的圈积的不可分解特征
Indecomposable characters of the wreath product of a torus by the infinite block-diagonal symmetric group
- B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine（乌克兰国家科学院B.维尔金低温物理与工程研究所）
- Institute of Science and Technology Austria (ISTA)（奥地利科学与技术研究所）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文完整描述了环面与对称群半直积的块对角归纳极限的不可分解特征，利用遍历方法证明分类，并应用于无限酉群的特征分类。
AI中文摘要：
本文获得了紧致N维环面T^N与对称群S_N的半直积T^N⋊S_N的“块对角”归纳极限的所有不可分解特征（中心正定函数）的完整描述。该分类通过Vershik和Kerov遍历方法的一种变体证明，即研究有限维子群特征的弱极限。作为我们结果的一个应用，我们给出了具有块对角嵌入的无限酉群的不可分解特征分类的另一个证明。
英文摘要：
In this paper we obtain a complete description of all indecomposable characters (central positive-definite functions) of "block-diagonal" inductive limits of semidirect products $\mathbb{T}^N\rtimes\mathfrak{S}_{N}$ of the compact $N$-dimensional torus $\mathbb{T}^{N}$ with the symmetric group $\mathfrak{S}_{N}$. The classification is proved by means of a variant of the ergodic method of Vershik and Kerov, namely by studying the weak limits of characters of finite-dimensional subgroups. As an application of our results, we give another proof of the classification of indecomposable characters of the infinite unitary group with block diagonal embeddings.
