论文标题
$ C^*$ - 流的球形表示II：表示系统和量子组设置
Spherical Representations of $C^*$-Flows II: Representation System and Quantum Group Setup
论文作者
论文摘要
本文是我们先前对操作员代数设置中球形表示的研究的续集。我们首先通过利用操作员系统及其亲戚的概念在本文中引入了维度组的可能类似物。然后，我们将研究应用于紧凑型量子基团的电感限制，并建立了Olshanski在量子组设置中的$ g <g <g \ times g $（通过对角线嵌入）形式的无限维gelfand对的球形单一表示概念的类似物。尤其是，这证明了萨托佐介对量子群的渐近表示理论的理由。
This paper is a sequel to our previous study of spherical representations in the operator algebra setup. We first introduce possible analogs of dimension groups in the present context by utilizing the notion of operator systems and their relatives. We then apply our study to inductive limits of compact quantum groups, and establish an analogue of Olshanski's notion of spherical unitary representations of infinite-dimensional Gelfand pairs of the form $G < G\times G$ (via the diagonal embedding) in the quantum group setup. This, in particular, justifies Ryosuke Sato's approach to asymptotic representation theory for quantum groups.
