Spherical Representations of *-Flows II: Representation System and Quantum Group Setup

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 comp...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2022
Main Author: Ueda, Yoshimichi
Format: Article
Language:English
Published: Інститут математики НАН України 2022
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/211618
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Spherical Representations of *-Flows II: Representation System and Quantum Group Setup. Yoshimichi Ueda. SIGMA 18 (2022), 050, 43 pages

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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Summary: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 < × (via the diagonal embedding) in the quantum group setup. This, in particular, justifies Ryosuke Sato's approach to asymptotic representation theory for quantum groups.
ISSN:1815-0659