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SPHERICAL REPRESENTATIONS FOR $\boldsymbol C^{\boldsymbol {*}}$-FLOWS III: WEIGHT-EXTENDED BRANCHING GRAPHS

Part of: Locally compact groups and their algebras Lie algebras and Lie superalgebras Lie groups

Published online by Cambridge University Press:  15 April 2024

YOSHIMICHI UEDA Open the ORCID record for YOSHIMICHI UEDA [Opens in a new window]
YOSHIMICHI UEDA*
Affiliation:
Graduate School of Mathematics, Nagoya University, Furocho, Chikusaku, Nagoya 464-8602, Japan
*
e-mail: ueda@math.nagoya-u.ac.jp
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Abstract

We apply Takesaki’s and Connes’s ideas on structure analysis for type III factors to the study of links (a short term of Markov kernels) appearing in asymptotic representation theory.

Keywords

C*-flowspherical representationKMS stateasymptotic representation theorybranching graphlinkK-theoryquantum group

MSC classification

Primary: 22D25: $C^*$-algebras and $W^*$-algebras in relation to group representations
Secondary: 22E66: Analysis on and representations of infinite-dimensional Lie groups 17B37: Quantum groups (quantized enveloping algebras) and related deformations
Type
Research Article
Information
Journal of the Australian Mathematical Society , First View , pp. 1 - 34
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

Communicated by Robert Yuncken

This work was supported by Grant-in-Aid for Scientific Research (B) JP18H01122.

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