Tetrahedron equation and quantum groups
| Project/Area Number |
15K13429
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Osaka City University |
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Principal Investigator |
OKADO Masato 大阪市立大学, 大学院理学研究科, 教授 (70221843)
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| Research Collaborator |
KUNIBA Atsuo
SERGEEV Sergey
KWON Jae-Hoon
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| Project Period (FY) |
2015-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | 可積分系 / ヤン・バクスター方程式 / 量子群 / 四面体方程式 / マルコフ過程 |
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| Outline of Final Research Achievements |
Tetrahedron equation, a 3-dimensional analogue of the Yang-Baxter equation that guarantees the integrability of a 2-dimensional lattice model, was investigated from representation theoretical aspect and a new symmetry which we call generalized quantum group and its representation was obtained. Applying the representation theory of quantum groups and explicit expressions of the solution of the tetrahedron equation to integrable Markov processes in probability theory, we also constructed several new integrable Markov processes and the matrix product formula of their stationary state.
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| Academic Significance and Societal Importance of the Research Achievements |
一般化量子群という新しい対称性を〝よい″表現とともに見つけ出した意義は大きい。これらの表現は今までに知られていた通常の量子展開環のよい表現と同様に、フュージョン構成法により高い次数の表現を構成することができたり、結晶基底が存在することが予想されるからである。この研究課題の補助期間は終わったが、ここで得られた一般化量子群の表現論の研究は今後も続け、一つの理論としてまとめ上げたいと考えている。
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Report
(5 results)
Research Products
(28 results)
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[Presentation] Crystal bases and rigged configurations2016
Author(s)
Masato Okado
Organizer
The 28th International Conference on Formal Power Series and Algebraic Combinatorics
Place of Presentation
Simon Fraser University, バンクーバー（カナダ）
Year and Date
2016-07-05
Related Report
Int'l Joint Research / Invited
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[Presentation] 多状態TAZRP2016
Author(s)
尾角正人
Organizer
日本数学会２０１６年度年会
Place of Presentation
筑波大学（茨城県・つくば市）
Year and Date
2016-03-19
Related Report
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