2023 Fiscal Year Final Research Report
Transformation of quantum symmetries based on asymptotic analysis in tensor categories
| Project/Area Number |
19K03539
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Review Section |
Basic Section 12010:Basic analysis-related
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| Research Institution | Nagoya University |
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Principal Investigator |
Yamagami Shigeru 名古屋大学, 多元数理科学研究科, 名誉教授 (90175654)
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| Project Period (FY) |
2019-04-01 – 2024-03-31
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| Keywords | free quantum state / hypergroup / radial representation |
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| Outline of Final Research Achievements |
We have investigated a variety of basic questions on transformation phenomena in quantum symmetries.Among them, the following topics are covered with results. Under the scaling transformation, asymptotic behaviours of free states
is described as approaching ground states.States of geometric series on a polynomial hypergroup is investigated and their spectrum analysis is worked out explicitly.As an application, Plancherel type decomposition is established for radial representations of free groups. Moreover the result is interpreted in terms of continued fractions and we have found that it exhibits a perturbation from the semicircular law.
In view of the role of radial representations in spectral decompositions, we focused on the description of the C*-algebra of radial representations and found that its primitive ideal space as well as its topology was captured in a concrete way.
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| Free Research Field |
量子解析
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| Academic Significance and Societal Importance of the Research Achievements |
スケール変換の下での自由状態の極限移行の形態は量子状態の漸近解析の手がかりを与えるものである。また、超群上の状態のスペクトル解析とその連分数展開による特徴づけは、量子確率論における新たな方向性を示唆している。非可換積分の基礎となる線型汎関数に伴う表現の記述は、従来敬遠されがちであった、その方面への初等的なアプローチを可能にするものと期待される。
自由群の放射表現に伴う作用素環の原始イデアル空間の記述は、非分離的位相の中でも従来の群表現によるものと対照的な構造を有するもので、その記述の簡明さと相まって、一定の役割を果たすものと思われる。
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