| 研究課題/領域番号 |
21F51028
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| 研究種目 |
特別研究員奨励費
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| 配分区分 | 補助金 |
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| 応募区分 | 外国 |
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| 審査区分 |
小区分11010:代数学関連
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| 研究機関 | 大阪公立大学 (2022)
大阪市立大学 (2021) |
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研究代表者 |
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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| 研究分担者 |
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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| 研究期間 (年度) |
2021-11-18 – 2024-03-31
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| 研究課題ステータス |
完了 (2022年度)
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| 配分額 *注記 |
2,300千円 (直接経費: 2,300千円)
2022年度: 1,100千円 (直接経費: 1,100千円)
2021年度: 800千円 (直接経費: 800千円)
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| キーワード | Crystal basis / Lie superalgebra / skew Howe duality |
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| 研究開始時の研究の概要 |
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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| 研究実績の概要 |
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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| 現在までの達成度 (段落) |
翌年度、交付申請を辞退するため、記入しない。
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| 今後の研究の推進方策 |
翌年度、交付申請を辞退するため、記入しない。
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