Supersymmetric rigged configurations and crystals of quantum affine supergroups
| Project/Area Number |
21F51028
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| Research Category |
Grant-in-Aid for JSPS Fellows
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| Allocation Type | Single-year Grants |
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| Section | 外国 |
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| Review Section |
Basic Section 11010:Algebra-related
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| Research Institution | Osaka Metropolitan University (2022)
Osaka City University (2021) |
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Principal Investigator |
尾角 正人 大阪公立大学, 大学院理学研究科, 教授 (70221843)
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| Co-Investigator(Kenkyū-buntansha) |
SCRIMSHAW TRAVIS 大阪公立大学, 大学院理学研究科, 外国人特別研究員
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| Project Period (FY) |
2021-11-18 – 2024-03-31
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| Project Status |
Completed (Fiscal Year 2022)
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| Budget Amount *help |
¥2,300,000 (Direct Cost: ¥2,300,000)
Fiscal Year 2022: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2021: ¥800,000 (Direct Cost: ¥800,000)
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| Keywords | Crystal basis / Lie superalgebra / skew Howe duality |
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| Outline of Research at the Start |
Our research deals with fermionic character formulas for the branching function for simple modules of the underlying finite-dimensional simple Lie algebra inside an affine highest weight module. It originates in the two-dimensional integrable lattice models in mathematical physics. We establish them through constructing a bijection between rigged configurations and Kirillov-Reshetikhin crystals. We also explore their super analogues.
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| Outline of Annual Research Achievements |
In addition to 2 papers on combinatorial representation theory being published, an additional 4 papers appeared on the arXiv preprint server, as follows.
I authored a paper on cellular subalgebras of the partition algebra. We described various diagram algebras and their representation theory using cellular algebras of Graham and Lehrer and the decomposition into half diagrams. We gave a new construction to build new cellular algebras from a general cellular algebra and subalgebras of the rook Brauer algebra that we call the cellular wreath product.
I coauthored a paper on a generalized definition for the quantum Clifford algebra introduced by Hayashi in 1990 using another parameter k that we call the twist, which was essential for my coauthor's subsequent work on quantum skew Howe duality and made a new connection with the alternative construction of Faddeev, Reshetikhin, and Takhtajan.
The second paper on rational lifting of crystal structures to study the ring of invariants was completed, building on our first paper from last year.
Lastly, the first of a series of at least 3 papers on the connection between Schubert calculus and stochastic particle processes was finished and uploaded.
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| Research Progress Status |
翌年度、交付申請を辞退するため、記入しない。
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| Strategy for Future Research Activity |
翌年度、交付申請を辞退するため、記入しない。
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Report
(2 results)
Research Products
(17 results)
