The application of tau-tilting theory to Hecke algebras
| Project/Area Number |
20J10492
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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 | 国内 |
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| Review Section |
Basic Section 11010:Algebra-related
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| Research Institution | Osaka University |
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Principal Investigator |
王 起 大阪大学, 情報科学研究科, 特別研究員(DC2)
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| Project Period (FY) |
2020-04-24 – 2022-03-31
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| Project Status |
Completed (Fiscal Year 2021)
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| Budget Amount *help |
¥1,700,000 (Direct Cost: ¥1,700,000)
Fiscal Year 2021: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2020: ¥900,000 (Direct Cost: ¥900,000)
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| Keywords | τ-tilting finiteness / Schur algebras / Gentle tree algebras / tau-tilting finite |
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| Outline of Research at the Start |
It is well-known that Hecke algebras of classical type are important in modular representation theory. We would like to classify block algebras of Hecke algebras of classical type in terms of tau-tilting theory, because tau-tilting theory is a powerful tool relating representation theory.
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| Outline of Annual Research Achievements |
In this academic year, I have written down three papers with my collaborators, the first one is jointed with Kengo Miyamoto on the τ-tilting finiteness of tensor products between simply connected algebras, the second one is jointed with Toshitaka Aoki on the τ-tilting finiteness of blocks of Schur algebras, the last one is jointed with Yingying Zhang on the number of support τ-tilting modules over trivial extensions of gentle tree algebras.
Through my own work and the collaboration with Aoki, I have got a complete result for the τ-tilting finiteness of Schur algebras. Since there is a deep connection between Schur algebras and Hecke algebras of type A, we have actually got some progress on this project.
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| Research Progress Status |
令和3年度が最終年度であるため、記入しない。
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| Strategy for Future Research Activity |
令和3年度が最終年度であるため、記入しない。
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Report
(2 results)
Research Products
(11 results)
